{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":1506,"title":"Maximum Intra-Vector Swaps","description":"This Challenge, based upon a contest in which Rokicki came in 2nd, is to find sequences containing 1:N that require maximum iterations prior to the value 1 appearing in the first position.\r\n\r\nThe processing rule is that positions 1 thru Vector(1) are swapped. Processing stops when Vector(1) is 1.\r\n\r\n*Example Sequences:* \r\n\r\n  [3 1 2], [2 1 3], [1 2 3] Score 2\r\n  [3 1 4 5 2][4 1 3 5 2][5 3 1 4 2][2 4 1 3 5][4 2 1 3 5][3 1 2 4 5][2 1 3 4 5][1 2 3 4 5]\r\n\r\n\r\n*Input:* n  (Integer from 1 to 31) (16 Actual Cases 2:11 13 17 19 23 29 31) \r\n\r\n*Output:* Vector of values 1:n\r\n\r\nExample:\r\n\r\nInput: 5  Output: [3 1 4 5 2]  \r\n\r\nScore: 7  \r\n\r\nA minimum cumulative score of 531 for the 17 cases is required to Pass.\r\n\r\nFinal Score = 2531 - sum(scores)\r\n\r\n*Hints:*\r\n\r\nUsage of perms for 10 or higher may cause Cody Memory/Time issues. Random subsets are suggested for n\u003e9.\r\n\r\nRequest: If Code is implemented external then please post as a block comment.\r\n\r\nFaster Code Block than fliplr:\r\n\r\n  function count=process_seq(seq)\r\n   count=0;\r\n   while seq(1)\u003e1\r\n    count=count+1;\r\n    seq(1:seq(1))=seq(seq(1):-1:1);\r\n   end\r\n  end","description_html":"\u003cp\u003eThis Challenge, based upon a contest in which Rokicki came in 2nd, is to find sequences containing 1:N that require maximum iterations prior to the value 1 appearing in the first position.\u003c/p\u003e\u003cp\u003eThe processing rule is that positions 1 thru Vector(1) are swapped. Processing stops when Vector(1) is 1.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample Sequences:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e[3 1 2], [2 1 3], [1 2 3] Score 2\r\n[3 1 4 5 2][4 1 3 5 2][5 3 1 4 2][2 4 1 3 5][4 2 1 3 5][3 1 2 4 5][2 1 3 4 5][1 2 3 4 5]\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e n  (Integer from 1 to 31) (16 Actual Cases 2:11 13 17 19 23 29 31)\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Vector of values 1:n\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003eInput: 5  Output: [3 1 4 5 2]\u003c/p\u003e\u003cp\u003eScore: 7\u003c/p\u003e\u003cp\u003eA minimum cumulative score of 531 for the 17 cases is required to Pass.\u003c/p\u003e\u003cp\u003eFinal Score = 2531 - sum(scores)\u003c/p\u003e\u003cp\u003e\u003cb\u003eHints:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eUsage of perms for 10 or higher may cause Cody Memory/Time issues. Random subsets are suggested for n\u003e9.\u003c/p\u003e\u003cp\u003eRequest: If Code is implemented external then please post as a block comment.\u003c/p\u003e\u003cp\u003eFaster Code Block than fliplr:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003efunction count=process_seq(seq)\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nend\r\n\u003c/pre\u003e","function_template":"function max_seq=find_max_swap_seq(n)\r\n max_seq=1:n;\r\n count=process_seq(max_seq);\r\nend\r\n\r\n% Suggested function for sequence performance evaluation\r\nfunction count=process_seq(seq)\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nend","test_suite":"tic\r\nfeval(@assignin,'caller','score',2000);\r\n%%\r\n% 2 1\r\nglobal cseq\r\ncseq{1}=1; % Gift answer\r\nmax_seq=find_max_swap_seq(2);\r\nassert(isequal(1:2,unique(max_seq)))\r\ncseq{2}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n% 3 2\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(3);\r\nassert(isequal(1:3,unique(max_seq)))\r\ncseq{3}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n% 4 4\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(4);\r\nassert(isequal(1:4,unique(max_seq)))\r\ncseq{4}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n% 5 7\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(5);\r\nassert(isequal(1:5,unique(max_seq)))\r\ncseq{5}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n% 6 10\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(6);\r\nassert(isequal(1:6,unique(max_seq)))\r\ncseq{6}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n% 7 16\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(7);\r\nassert(isequal(1:7,unique(max_seq)))\r\ncseq{7}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n% 8 22\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(8);\r\nassert(isequal(1:8,unique(max_seq)))\r\ncseq{8}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n% 9 30\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(9);\r\nassert(isequal(1:9,unique(max_seq)))\r\ncseq{9}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n%10 38\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(10);\r\nassert(isequal(1:10,unique(max_seq)))\r\ncseq{10}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n%11 51\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(11);\r\nassert(isequal(1:11,unique(max_seq)))\r\ncseq{11}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n%13 80 case 12\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(13);\r\nassert(isequal(1:13,unique(max_seq)))\r\ncseq{12}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n%17 159 case 13\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(17);\r\nassert(isequal(1:17,unique(max_seq)))\r\ncseq{13}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n%19 221 case 14\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(19);\r\nassert(isequal(1:19,unique(max_seq)))\r\ncseq{14}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n%23 382 case 15\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(23);\r\nassert(isequal(1:23,unique(max_seq)))\r\ncseq{15}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n%29 689 case 16\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(29);\r\nassert(isequal(1:29,unique(max_seq)))\r\ncseq{16}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n%31 819 case 17\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(31);\r\nassert(isequal(1:31,unique(max_seq)))\r\ncseq{17}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\ntoc\r\n%%\r\nglobal cseq\r\ntotal=0;\r\nfor i=2:17\r\n seq=cseq{i};\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\n total=total+count;\r\nend\r\n\r\n% 2531 is optimal sum\r\ntotal=sum([0 1 2 4 7 10 16 22 30 38 51 80 159 221 382 689 819])-total;\r\nassert(total\u003c2001); % Minimum performance requirement\r\n\r\ntoc\r\nfeval(@assignin,'caller','score',min(2000,total));\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-05-13T01:28:12.000Z","updated_at":"2026-04-01T14:34:03.000Z","published_at":"2013-05-13T04:01:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge, based upon a contest in which Rokicki came in 2nd, is to find sequences containing 1:N that require maximum iterations prior to the value 1 appearing in the first position.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe processing rule is that positions 1 thru Vector(1) are swapped. Processing stops when Vector(1) is 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample Sequences:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[3 1 2], [2 1 3], [1 2 3] Score 2\\n[3 1 4 5 2][4 1 3 5 2][5 3 1 4 2][2 4 1 3 5][4 2 1 3 5][3 1 2 4 5][2 1 3 4 5][1 2 3 4 5]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e n (Integer from 1 to 31) (16 Actual Cases 2:11 13 17 19 23 29 31)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Vector of values 1:n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: 5 Output: [3 1 4 5 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eScore: 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA minimum cumulative score of 531 for the 17 cases is required to Pass.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFinal Score = 2531 - sum(scores)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsage of perms for 10 or higher may cause Cody Memory/Time issues. Random subsets are suggested for n\u0026gt;9.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRequest: If Code is implemented external then please post as a block comment.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFaster Code Block than fliplr:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[function count=process_seq(seq)\\n count=0;\\n while seq(1)\u003e1\\n  count=count+1;\\n  seq(1:seq(1))=seq(seq(1):-1:1);\\n end\\nend]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42715,"title":" Throw common elements of two vector arrays in sorted manner","description":"\r\nThrow common elements as output in sorted manner (acending order) of two given input vector arrays","description_html":"\u003cp\u003eThrow common elements as output in sorted manner (acending order) of two given input vector arrays\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nA = [1 2 3 4 5 6 7 8];\r\nB = [4 5 6 6 7 0 12 34];\r\ny_correct = [7 6 5 4];\r\nassert(isequal(your_fcn_name(A,B),y_correct))\r\n\r\n%%\r\nA = [1 2 3 4 5 6 71 8];\r\nB = [4 5 6 6 7 0 12 34];\r\ny_correct = [6 5 4];\r\nassert(isequal(your_fcn_name(A,B),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":46868,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":74,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-01-15T10:10:48.000Z","updated_at":"2026-02-28T08:11:04.000Z","published_at":"2016-01-15T10:17:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThrow common elements as output in sorted manner (acending order) of two given input vector arrays\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60286,"title":"Hofstadter Q sequence","description":"The Hofstadter Q sequence is defined as follows:\r\n\r\nThe first elements of the sequence are 1, 1, 2, 3, 3, 4, 5, 5, 6, 6.\r\nWrite a function to compute  for a given n.\r\nSee https://oeis.org/A005185","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 170.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343.5px 85.45px; transform-origin: 343.5px 85.45px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.5px; text-align: left; transform-origin: 320.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Hofstadter Q sequence is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 49.4px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 24.7px; text-align: left; transform-origin: 320.5px 24.7px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-19px\"\u003e\u003cimg 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7ydESbGRwD53GGBAaTiEXOw3bzFYiouABfN+bBRCnm0OXpASdjRMFGhvlwy8CZu6jaSPFAKEcRwZWu2tqkyh1y3o9yFR9o25MccpSWmS9HoYyeoYiiSZPtojsYRsM0lNxDM7K/yd7Rv/ksNKds9/FmCHHQ/DOJVwSNMjm4dQmvdFsDkkMWbBO4r3kzRLnAQQ2ryCxni+iYXkQ4EGSa72Ikm2LQqSEIBPwd53RNA6Hw5OwywhEC5j4shhnE58oOYJ2i4l8dh2T80uWZokvR5KrMwCfQxJkuQn4+2EKElL5EVDY4QEd61I864V4WH4/0kER6fQn0XThiRxEhBSxIFlbOew7xGkDjHQ39iFeXOOEHZGig7fI/LSeU5o39SLJL4UYmQ+TZlGaJzYKcEW8qVC0PmCjPcu6Gl+vyQccE3xnSn2j7G/ZOwPo+X4SpMkt/d6aPkQ+mg+JEkyH+5PFXJsjGh/aJU4LPiXWEpeJLaVTU4M+qJiM15yvKecFU7Ri5Tn3Tb7pQ+sc/ukyjjH+IIJqYkUOD5xaGkQ6ItaxIaSH3/vwAStkRc55XmT5VSvO5mILmec2ENxpCUhX/yUDWXdUqUiKjehbXLNEIL5gY8F5zWVjI7ogyTBZ6j1wHzwAeQIyR2Eoq3TesDRyXldKB+8Y9SoZffJ+txBhibJNBg8ymThsH3kZa1X+Vn0kKgryYuWtt94u7F5UXwWjQbBOfT8yBE/Oudpj6gN5dIgSrDBiJ8TEoT9tp7eiQcZUqAkHcHQyGvDsTIb80dhjZRL3wQD9uRUZAQNPjlp+CihLc4Tdg1kA3E8B89p1YImjUZN4gLEQwhZwqTEWFJSQ8oGK9FnvY9Vr4ebhBKTMw/e2WOi4TqsB+Z2cNj9Ge8NK0XiLJX/gvOiULZGR5JsqamszZedIxvwjjYRAnnN2CfxjKeHw9EGbE94UdFEEQrR4sBAi1kXwRaFNoyGzZaY2EK21U3aNBXd2fLePSbKMRt8GNiaUxQE4aOI9gjOJYmK+3BYGyTLV3lWMB9gZyWlFDLe6Wu9godDWBXrIlVxL02SfU3B66EssoTZQYYQ4++jaz6aFJPhAEJMVB+v33JITZIzWdDy0C7qAkHyMrEVYrB4Tck+QfXHgcPWmSMcUJeTs4cXlJeTFyC9/MQR8je2hWyv0CQ46XHMQh1IiJ2A7Lr8MXBA8wET8IHssL3izYcYeZkg1uQ0SdWS6pXN0R4hq6uFOQJ86HtZ4bgNzhuaF/PKc2bMECjENM9Bt+z921yfitiuA0l6PbR5snltWaOE2KVK/ukqzFJE2hAR8oIxkCShOhxRcIp4WXnBcSik/NdF02VrDenhlKlrI2hRlDdDY0x2ppTnDanSNwQ6hAaT9+i2HaHLQ4K0IBLMCcRNpnzuRf2gSVP0mA9OXdsEJzRR+kmaecrzJo6RLQcfjxKCZo/Gix0Zok5e+TNEOBBmEYh8npZZ4v5t+lgXkvR6aPNU89uyw4IHZiNH0tlZO/kvhtIkOf4UJ0S9OAUEydcd+xkqLy8eLzgvPltwnDLEPc4zthOcThA4zohEFKQxonFhI7t5Ze8kX3yswseCLxghMnWbIhoyWBDryTaVkB7a4rUnIoBq5NhWCL2ZFeyY2A552ZJcO8q3EVaFh7lkIQyeF1XqGTMZVBT+5flha67X/6yPExshWi3aMCFJjIu4T8KEiOHkuZWWdSDJTVwPQ8c64w9B0cBkt8PHfCiSzF342A8gvUWxkbn9TKkdi6nJZjvUfNnOQ9qELn1ngR0VUwLhXDxTni/2V8iSDxyHwFGDE+85Hn7siHwQSso6kGSb+U5pPQwZ68z2+zehrOyA/9hJss1icdthESDThpAtTAWQIPZfguPR5rEpczwHnnp+r5+uyUFwfAiJC8W2iYYMUaJdpvOPSs5saiRZEpuSfXVZD0PFOmPWwsGJuS4VZNmOhUmy5LLYzL5YQ0QasL1m2090ASYTjON1gTQJyap7DtEUWZTEqGGjTtXqIdXDZr7qxHkS/5ojkC126nliksxBsHubZdZDm1jnUuuB3Qzr7oCZ41NMkt3XgK+cgwCRB7OpiGiBnPbIb9hG58VPplJvLFIcPghfdeyp/P9EmvydvnKPtEBbTUfszg7XJNn/Eu66HtrEOpdaD3zgyUpLp43uhE5XTRIPUKrcM8U83P6Xke8AAilmka01oUkIoRgUDkYzTTGwJdEySZZEs2xfq451pogInu66+acYSRJr9InojW0R7nOLEWiLABomjpl6sD/aY/Lq4wiiTUkxSZZEs1xfq451JhGFRBMiMupCPDX/w1b+f+mqSWJLIvaNsB3c5cTD2QNdbsFsQk8ElxMQj0ebVMUkZEGQwkh4GFvm0meqY/vkBSEcCmeRZRwIrDLWmWf/4lhn9dhi6g9QKYsIjJS115kkgZWagSkGD4MrqT4WI5CLAN7PlEfOWeFJWEdkmtwl81iP3PvRJ+uVIgYUDCGW89lVDVLOStr+QuR25nbFEVhVrDNJJuyCyQSbJ8RiY/LZLl01STqg3mEK7MZ9TniHxQgYASMwKQSWIUmA4HxnUt8QSp2lQ6kmBZInYwSMwOYisCxJYmzFZkRMHPYl9vJDFzDY3KfpmRsBI1AcgWVJkgFdJAobcI4KhTexTzZVzC4+EXdoBIyAEegDgRIkybgI4cAATtFXgoap1VYvXtHH2N2nETACRqB3BEqRJAPlBD5slKSkUal63zhqoPdJ+AZGwAgYgb4QKEmSaYw4csiD5NTCdaoI3hfG7tcIGIE1RqAPklxjODx0I2AEjMCOCJgkvSKMgBEwAlsg8D8GW5Ovv5jJuAAAAABJRU5ErkJggg==\" width=\"164.5\" height=\"49.5\" style=\"width: 164.5px; height: 49.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.5px; text-align: left; transform-origin: 320.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first elements of the sequence are 1, 1, 2, 3, 3, 4, 5, 5, 6, 6.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 11.25px; text-align: left; transform-origin: 320.5px 11.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003efor a given\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.5px; text-align: left; transform-origin: 320.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSee \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A005185\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://oeis.org/A005185\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function q = Q_sequence(n)\r\n\r\nend","test_suite":"all_glo = [1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 6, 8, 8, 8, 10, 9, 10, 11, 11, 12, 12, 12, 12, 16, 14, 14, 16, 16, 16, 16, 20, 17, 17, 20, 21, 19, 20, 22, 21, 22, 23, 23, 24, 24, 24, 24, 24, 32, 24, 25, 30, 28, 26, 30, 30, 28, 32, 30, 32, 32, 32, 32, 40, 33, 31, 38, 35, 33, 39, 40, 37, 38, 40, 39, 40, 39, 42, 40, 41, 43, 44, 43, 43, 46, 44, 45, 47, 47, 46, 48, 48, 48, 48, 48, 48, 64, 41, 52, 54, 56, 48, 54, 54, 50, 60, 52, 54, 58, 60, 53, 60, 60, 52, 62, 66, 55, 62, 68, 62, 58, 72, 58, 61, 78, 57, 71, 68, 64, 63, 73, 63, 71, 72, 72, 80, 61, 71, 77, 65, 80, 71, 69, 77, 75, 73, 77, 79, 76, 80, 79, 75, 82, 77, 80, 80, 78, 83, 83, 78, 85, 82, 85, 84, 84, 88, 83, 87, 88, 87, 86, 90, 88, 87, 92, 90, 91, 92, 92, 94, 92, 93, 94, 94, 96, 94, 96, 96, 96, 96, 96, 96, 128, 72, 96, 115, 100, 84, 114, 110, 93, 106, 124, 82, 101, 111, 108, 118, 104, 108, 106, 114, 104, 114, 109, 100, 109, 120, 112, 108, 118, 106, 105, 130, 110, 114, 115, 112, 107, 120, 114, 122, 121, 120, 114, 138, 110, 122, 119, 120, 130];\r\nn = randi([90,numel(all_glo)]) \r\ny_correct = all_glo(n)\r\n\r\n%%\r\n% Only for this random test, n and y_correct are displayed but their definition is hidden.\r\nn\r\ny_obtained = Q_sequence(n)\r\ny_correct\r\nassert(isequal(y_obtained,y_correct));\r\n\r\n\r\n%%\r\nn = 73\r\ny_obtained = Q_sequence(n)\r\ny_correct = 40\r\nassert(isequal(y_obtained,y_correct));\r\n\r\n%%\r\nyy_correct = [1,1,2,3,3,4,5,5,6,6,6,8,8,8,10,9,10,11,11,12,12];\r\nfor n = 1:numel(yy_correct)\r\n    y_obtained = Q_sequence(n);\r\n    y_correct = yy_correct(n);\r\n    assert(isequal(y_obtained,y_correct));\r\nend","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":208445,"edited_by":208445,"edited_at":"2024-06-09T15:57:38.000Z","deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":"2024-05-11T18:02:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-11T17:54:45.000Z","updated_at":"2026-03-01T15:18:23.000Z","published_at":"2024-05-11T18:02:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Hofstadter Q sequence is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$$\\\\begin{cases}\\nQ_1 = Q_2 = 1\\\\\\\\\\nQ_n = Q_{n-Q_{n-1}}+Q_{n-Q_{n-2}}\\n\\\\end{cases}$$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first elements of the sequence are 1, 1, 2, 3, 3, 4, 5, 5, 6, 6.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003efor a given\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A005185\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://oeis.org/A005185\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1655,"title":"Sum of first n positive integers","description":"Given n, find the sum of first n positive integers\r\nExample: If n=10, then x=1,2,3,4,5,6,7,8,9,10. The sum of these terms is 55","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 148px 8px; transform-origin: 148px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven n, find the sum of first n positive integers\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 236.5px 8px; transform-origin: 236.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample: If n=10, then x=1,2,3,4,5,6,7,8,9,10. The sum of these terms is 55\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = summation(n)\r\n y=n;\r\nend","test_suite":"%%\r\nn = 10;\r\ny = 55;\r\nassert(isequal(summation(n),y))\r\n%%\r\nn = 0;\r\ny = 0;\r\nassert(isequal(summation(n),y))\r\n%%\r\nn = 17;\r\ny = 153;\r\nassert(isequal(summation(n),y))\r\n%%\r\nn = 100;\r\ny = 5050;\r\nassert(isequal(summation(n),y))\r\n%%\r\nn = 1000;\r\ny = 500500;\r\nassert(isequal(summation(n),y))","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":14636,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":622,"test_suite_updated_at":"2021-09-27T15:20:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-19T05:26:57.000Z","updated_at":"2026-02-06T18:34:50.000Z","published_at":"2013-06-19T05:30:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven n, find the sum of first n positive integers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: If n=10, then x=1,2,3,4,5,6,7,8,9,10. The sum of these terms is 55\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44818,"title":"Add consecutive integer numbers","description":"Given consecutive numbers, add the numbers *without using the sum command in MATLAB.*","description_html":"\u003cp\u003eGiven consecutive numbers, add the numbers \u003cb\u003ewithout using the sum command in MATLAB.\u003c/b\u003e\u003c/p\u003e","function_template":"function y = add_consecutive_integers(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(add_consecutive_integers(x),y_correct))\r\n\r\n%%\r\nx = 1:10;\r\ny_correct = sum(x);\r\nassert(isequal(add_consecutive_integers(x),y_correct))\r\n\r\n%%\r\nx = 5:10;\r\ny_correct = sum(x);\r\nassert(isequal(add_consecutive_integers(x),y_correct))\r\n\r\n%%\r\nx = 50:100;\r\ny_correct = sum(x);\r\nassert(isequal(add_consecutive_integers(x),y_correct))\r\n\r\n\r\n%% \r\nassessFunctionAbsence('sum','Filename','add_consecutive_integers')","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":265425,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":58,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":677,"created_at":"2019-01-04T22:24:50.000Z","updated_at":"2026-02-17T21:08:18.000Z","published_at":"2019-01-04T22:25:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven consecutive numbers, add the numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewithout using the sum command in MATLAB.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":48005,"title":"number play","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 111px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 55.5px; transform-origin: 407px 55.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFrom the sequence 3,8,13,18,23,28,33,38.....\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eif the input n=2 output should be y=[13 18]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                  n=6;y=[53 58]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = seq(n)\r\n  y = ;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = [3 8];\r\nassert(isequal(seq(n),y_correct))\r\n%%\r\nn = 5;\r\ny_correct = [43 48];\r\nassert(isequal(seq(n),y_correct))\r\n%%\r\nn = 200;\r\ny_correct = [1993 1998];\r\nassert(isequal(seq(n),y_correct))\r\n%%\r\nn = 501;\r\ny_correct = [5003 5008];\r\nassert(isequal(seq(n),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":628208,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":51,"test_suite_updated_at":"2020-12-17T06:48:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-17T06:40:21.000Z","updated_at":"2026-02-19T15:40:04.000Z","published_at":"2020-12-17T06:48:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFrom the sequence 3,8,13,18,23,28,33,38.....\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eif the input n=2 output should be y=[13 18]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                  n=6;y=[53 58]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61168,"title":"Find record values in a sequence","description":"Write a function to find the record values in a sequence—that is, the largest values seen since the start. For example, if the sequence is\r\n1, 2, 0, 4, 5, 3, 7, 8, 6, 10, 11, 9, 13, 14, 12, 16\r\nthen the function should return\r\n1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 66px; transform-origin: 408px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find the record values in a sequence—that is, the largest values seen since the start. For example, if the sequence is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e1, 2, 0, 4, 5, 3, 7, 8, 6, 10, 11, 9, 13, 14, 12, 16\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen the function should return\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = records(x)\r\n  y = sort(x,'descending');\r\nend","test_suite":"%%  Example (tersum n+n)\r\nx = [1 2 0 4 5 3 7 8 6 10 11 9 13 14 12 16];\r\ny = records(x);\r\ny_correct = [1 2 4 5 7 8 10 11 13 14 16];\r\nassert(isequal(y,y_correct))\r\n\r\n%%  Prime gaps\r\nx = [1 2 2 4 2 4 2 4 6 2 6 4 2 4 6 6 2 6 4 2 6 4 6 8 4 2 4 2 4 14 4 6 2 10 2 6 6 4 6 6 2 10 2 4 2 12 12 4 2 4 6 2 10 6 6 6 2 6 4 2 10 14 4 2 4 14 6 10 2 4 6 8 6 6 4 6 8 4 8 10 2 10 2 6 4 6 8 4 2 4 12 8 4 8 4 6 12 2 18 6];\r\ny = records(x);\r\ny_correct = [1 2 4 6 8 14 18];\r\nassert(isequal(y,y_correct))\r\n\r\n%%  Numbers of divisors\r\nx = [1 2 2 3 2 4 2 4 3 4 2 6 2 4 4 5 2 6 2 6 4 4 2 8 3 4 4 6 2 8 2 6 4 4 4 9 2 4 4 8 2 8 2 6 6 4 2 10 3 6 4 6 2 8 4 8 4 4 2 12 2 4 6 7 4 8 2 6 4 8 2 12 2 4 6 6 4 8 2 10 5 4 2 12 4 4 4 8 2 12 4 6 4 4 4 12 2 6 6 9];\r\ny = records(x);\r\ny_correct = [1 2 3 4 6 8 9 10 12];\r\nassert(isequal(y,y_correct))\r\n\r\n%%  Length of the period of the continued fraction of (1+sqrt(n))/2\r\nx = [0 2 2 0 1 4 4 4 0 2 2 2 1 4 2 0 3 6 6 4 2 6 4 4 0 2 2 4 1 2 8 4 4 4 2 0 3 6 6 8 5 4 10 6 2 8 4 4 0 2 2 4 1 6 4 2 6 6 6 4 3 4 2 0 3 6 10 6 4 6 8 4 9 6 4 8 2 4 4 4 0 2 2 2 1 6 2 8 7 2 8 8 2 12 4 8 9 4 2 0];\r\ny = records(x);\r\ny_correct = [0 2 4 6 8 10 12];\r\nassert(isequal(y,y_correct))\r\n\r\n%%  Numbers of ways n can be properly factored\r\nx = [0 0 0 1 0 1 0 2 1 1 0 3 0 1 1 4 0 3 0 3 1 1 0 6 1 1 2 3 0 4 0 6 1 1 1 8 0 1 1 6 0 4 0 3 3 1 0 11 1 3 1 3 0 6 1 6 1 1 0 10 0 1 3 10 1 4 0 3 1 4 0 15 0 1 3 3 1 4 0 11 4 1 0 10 1 1 1 6 0 10 1 3 1 1 1 18 0 3 3 8];\r\ny = records(x);\r\ny_correct = [0 1 2 3 4 6 8 11 15 18];   \r\nassert(isequal(y,y_correct))\r\n\r\n%%  Numbers of ways n can be properly factored\r\nx = [1 1 1 2 1 1 1 3 2 1 1 2 1 1 1 4 1 2 1 2 1 1 1 3 2 1 3 2 1 1 1 5 1 1 1 4 1 1 1 3 1 1 1 2 2 1 1 4 2 2 1 2 1 3 1 3 1 1 1 2 1 1 2 6 1 1 1 2 1 1 1 6 1 1 2 2 1 1 1 4 4 1 1 2 1 1 1 3 1 2 1 2 1 1 1 5 1 2 2 4 1 1 1 3 1 1 1 6 1 1 1 4 1 1 1 2 2 1 1 3 2 1 1 2 3 2 1 7 1 1 1 2 1 1 3 3 1 1 1 2 1 1 1 8 1 1 2 2 1 2 1 3 2 1 1 2 1 1 1 5 1 4 1 2 1 1 1 3 2 1 2 2 1 1 2 4 1 1 1 4 1 1 1 3 1 1 1 2 3 1 1 6 1 1 1 4 1 2 1 6];\r\ny = records(x);\r\ny_correct = 1:8;   \r\nassert(isequal(y,y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2026-01-20T02:33:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-20T02:33:28.000Z","updated_at":"2026-02-18T21:58:32.000Z","published_at":"2026-01-20T02:33:49.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find the record values in a sequence—that is, the largest values seen since the start. For example, if the sequence is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 0, 4, 5, 3, 7, 8, 6, 10, 11, 9, 13, 14, 12, 16\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen the function should return\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44225,"title":"Sum of self power series","description":"The series, 1^1,2^2,3^3,4^4,....\r\n\r\nFind the sum of such series when x terms are given.","description_html":"\u003cp\u003eThe series, 1^1,2^2,3^3,4^4,....\u003c/p\u003e\u003cp\u003eFind the sum of such series when x terms are given.\u003c/p\u003e","function_template":"function y = sumofseries(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(sumofseries(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 5;\r\nassert(isequal(sumofseries(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 288;\r\nassert(isequal(sumofseries(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":134801,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":81,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-05-25T05:40:41.000Z","updated_at":"2026-03-10T15:08:41.000Z","published_at":"2017-05-25T05:40:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe series, 1^1,2^2,3^3,4^4,....\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the sum of such series when x terms are given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42833,"title":"Return the sequence element I","description":"Given a positive integer, x, return a positive integer, y, which is the xth term in the sequence [1 2 2 3 3 3...], in which one instance of the number 1 is followed by two instances of the number 2, followed by three instances of the number 3, and so on.\r\n\r\nExample 1:\r\n\r\nx = 5\r\n\r\ny = 3\r\n\r\nExample 2:\r\n\r\nx = 105\r\n\r\ny = 14","description_html":"\u003cp\u003eGiven a positive integer, x, return a positive integer, y, which is the xth term in the sequence [1 2 2 3 3 3...], in which one instance of the number 1 is followed by two instances of the number 2, followed by three instances of the number 3, and so on.\u003c/p\u003e\u003cp\u003eExample 1:\u003c/p\u003e\u003cp\u003ex = 5\u003c/p\u003e\u003cp\u003ey = 3\u003c/p\u003e\u003cp\u003eExample 2:\u003c/p\u003e\u003cp\u003ex = 105\u003c/p\u003e\u003cp\u003ey = 14\u003c/p\u003e","function_template":"function y = seqelem(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('seqelem.m');\r\nassert(isempty(strfind(filetext,'feval')))\r\nassert(isempty(strfind(filetext,'polyval')))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 3;\r\nassert(isequal(seqelem(x),y_correct))\r\n\r\n%%\r\nx = 105;\r\ny_correct = 14;\r\nassert(isequal(seqelem(x),y_correct))\r\n\r\n%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(seqelem(x),y_correct))\r\n\r\n%%\r\nx = 5040;\r\ny_correct = 100;\r\nassert(isequal(seqelem(x),y_correct))\r\n\r\n%%\r\nx = 96669;\r\ny_correct = 440;\r\nassert(isequal(seqelem(x),y_correct))\r\n\r\n%%\r\nx = 9999991;\r\ny_correct = 4472;\r\nassert(isequal(seqelem(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-26T15:10:19.000Z","updated_at":"2026-02-28T08:12:49.000Z","published_at":"2016-04-26T15:10:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a positive integer, x, return a positive integer, y, which is the xth term in the sequence [1 2 2 3 3 3...], in which one instance of the number 1 is followed by two instances of the number 2, followed by three instances of the number 3, and so on.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 105\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = 14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":48030,"title":"Find the Pattern 3","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 171px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 85.5px; transform-origin: 407px 85.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the pattern for the following sequence:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(2) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(11) = 143\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(15) = 255\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(17) = 323\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCreate a function which satisfies the pattern shown above.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pat(x)\r\n  y = x/2;\r\nend","test_suite":"%%\r\nx = 2;\r\ny_correct = 8;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 11;\r\ny_correct = 143;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 17;\r\ny_correct = 323;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 212;\r\ny_correct = 45368;\r\nassert(isequal(pat(x),y_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":251,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-17T19:27:48.000Z","updated_at":"2026-03-20T14:59:15.000Z","published_at":"2020-12-17T19:27:48.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the pattern for the following sequence:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(2) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(11) = 143\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(15) = 255\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(17) = 323\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a function which satisfies the pattern shown above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43684,"title":"0, 2, 0, -2, 0, 2, 0, -2, ...","description":"Generate the first n terms of a periodic sequence defined as\r\n\r\n  f(x) = 0, 2, 0, -2, 0, 2, 0, -2, ..., for x = 1, 2, 3, 4, 5, 6, 7, 8, ...","description_html":"\u003cp\u003eGenerate the first n terms of a periodic sequence defined as\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ef(x) = 0, 2, 0, -2, 0, 2, 0, -2, ..., for x = 1, 2, 3, 4, 5, 6, 7, 8, ...\r\n\u003c/pre\u003e","function_template":"function y = seq(n)\r\n  y = n;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = [0];\r\nassert(isequal(seq(n),y_correct))\r\n\r\n%%\r\nn = 4\r\ny_correct = [0, 2, 0, -2];\r\nassert(isequal(seq(n),y_correct))\r\n\r\n%%\r\nn = 5\r\ny_correct = [0, 2, 0, -2, 0];\r\nassert(isequal(seq(n),y_correct))\r\n\r\n%%\r\nn = 8\r\ny_correct = [0, 2, 0, -2, 0, 2, 0, -2];\r\nassert(isequal(seq(n),y_correct))\r\n\r\n%%\r\nn = 25\r\ny_correct = [0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0];\r\nassert(isequal(seq(n),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":81,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-11-26T20:23:48.000Z","updated_at":"2026-02-26T12:18:36.000Z","published_at":"2016-11-26T20:25:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGenerate the first n terms of a periodic sequence defined as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[f(x) = 0, 2, 0, -2, 0, 2, 0, -2, ..., for x = 1, 2, 3, 4, 5, 6, 7, 8, ...]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":48065,"title":"Find the Pattern 10","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 171px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 85.5px; transform-origin: 407px 85.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the pattern for the following sequence:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(1) = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(2) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(3) = 25\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(7) = 169\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCreate a function which satisfies the pattern shown above.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pat(x)\r\n  y = x+tan(x);\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 2;\r\ny_correct = 9;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 5;\r\ny_correct = 81;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 11;\r\ny_correct = 441;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 7;\r\ny_correct = 169;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 25;\r\ny_correct = 2401;\r\nassert(isequal(pat(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":244,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-17T20:13:51.000Z","updated_at":"2026-03-20T15:10:27.000Z","published_at":"2020-12-17T20:13:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the pattern for the following sequence:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(2) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(3) = 25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(7) = 169\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a function which satisfies the pattern shown above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54770,"title":"Count the peaceful queens","description":"In a 5x5 chessboard with a queen of one color (white, say) on the perimeter, one can place 12 black queens on the board such that none of the black queens can attack the white one (or vice versa). \r\nWrite a function that returns the number of queens that cannot attack a queen of the other color placed anywhere on the perimeter of an x chessboard.  \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 328.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 164.35px; transform-origin: 407px 164.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.1833px 8px; transform-origin: 85.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn a 5x5 chessboard with a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Queen_(chess)#Placement_and_movement\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003equeen\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 272.283px 8px; transform-origin: 272.283px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of one color (white, say) on the perimeter, one can place 12 black queens on the board such that none of the black queens can attack the white one (or vice versa). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 372.883px 8px; transform-origin: 372.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the number of queens that cannot attack a queen of the other color placed anywhere on the perimeter of an \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.5px 8px; transform-origin: 3.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.0083px 8px; transform-origin: 42.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e chessboard. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 226.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 113.35px; text-align: left; transform-origin: 384px 113.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 764px;height: 221px\" 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\" data-image-state=\"image-loaded\" width=\"764\" height=\"221\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = peacefulQueens(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 5;\r\nassert(isequal(peacefulQueens(n),12))\r\n\r\n%%\r\nn = 8;\r\nassert(isequal(peacefulQueens(n),42))\r\n\r\n%%\r\nn = 64;\r\nassert(isequal(peacefulQueens(n),3906))\r\n\r\n%%\r\nn = 4096;\r\nassert(isequal(peacefulQueens(n),16764930))\r\n\r\n%%\r\nn = 262144;\r\nassert(isequal(peacefulQueens(n),68718690306))\r\n\r\n%%\r\nn = 2097152;\r\nassert(isequal(peacefulQueens(n),4398040219650))\r\n\r\n%%\r\nn = 16777216;\r\nassert(isequal(peacefulQueens(n),281474926379010))\r\n\r\n%%\r\nm = randi(1000)+4;\r\ny = sum(arrayfun(@peacefulQueens,3:m));\r\nassert(isequal(y,polyval([1 3 2 0],m-2)/3))\r\n\r\n%%\r\nfiletext = fileread('peacefulQueens.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-07-02T17:52:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":76,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-07-02T02:16:14.000Z","updated_at":"2026-01-26T15:48:57.000Z","published_at":"2022-07-02T02:17:02.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a 5x5 chessboard with a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Queen_(chess)#Placement_and_movement\\\"\u003e\u003cw:r\u003e\u003cw:t\u003equeen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of one color (white, say) on the perimeter, one can place 12 black queens on the board such that none of the black queens can attack the white one (or vice versa). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the number of queens that cannot attack a queen of the other color placed anywhere on the perimeter of an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54675,"title":"Define an arithmetic sequence","description":"Given three numbers n, a, and d, define an arithmetic sequence of n terms with a being the initial term of the sequence and d being the common difference of the sequence. If n = 0, then return an empty array since there would be no terms in the sequence.\r\nExamples:\r\nInput  [n,a,d] = deal(10,5,2)\r\nOutput seq = [5 7 9 11 13 15 17 19 21 23]\r\n\r\nInput  [n,a,d] = deal(5,2,-3)\r\nOutput seq = [2 -1 -4 -7 -10]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 225.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 112.875px; transform-origin: 407px 112.875px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven three numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, define an arithmetic sequence of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e terms with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e being the initial term of the sequence and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e being the common difference of the sequence. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e = 0, then return an empty array since there would be no terms in the sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4375px; transform-origin: 404px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eInput  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003e[n,a,d] = deal(10,5,2)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eseq = [5 7 9 11 13 15 17 19 21 23]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4375px; transform-origin: 404px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eInput  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003e[n,a,d] = deal(5,2,-3)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eseq = [2 -1 -4 -7 -10]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function seq = arithSequence(n,a,d)\r\n    seq = [n a d];\r\nend","test_suite":"%%\r\n[n,a,d] = deal(10,5,2);\r\nseq_correct = [5 7 9 11 13 15 17 19 21 23];\r\nassert(isequal(arithSequence(n,a,d),seq_correct))\r\n%%\r\n[n,a,d] = deal(5,2,-3);\r\nseq_correct = [2 -1 -4 -7 -10];\r\nassert(isequal(arithSequence(n,a,d),seq_correct))\r\n%%\r\n[n,a,d] = deal(7,3,0.5);\r\nseq_correct = [3 3.5 4 4.5 5 5.5 6];\r\nassert(isequal(arithSequence(n,a,d),seq_correct))\r\n%%\r\n[n,a,d] = deal(0, 1, 2);\r\nassert(isempty(arithSequence(n,a,d)))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":792819,"edited_by":792819,"edited_at":"2022-05-24T21:17:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-05-24T21:17:06.000Z","updated_at":"2026-03-05T13:32:48.000Z","published_at":"2022-05-24T21:17:27.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven three numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, define an arithmetic sequence of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e terms with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e being the initial term of the sequence and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e being the common difference of the sequence. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e = 0, then return an empty array since there would be no terms in the sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Input  [n,a,d] = deal(10,5,2)\\nOutput seq = [5 7 9 11 13 15 17 19 21 23]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Input  [n,a,d] = deal(5,2,-3)\\nOutput seq = [2 -1 -4 -7 -10]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":48020,"title":"Find the Pattern 1","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 141px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 70.5px; transform-origin: 407px 70.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the pattern for the following sequence:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(1) = 10\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(3) = 16\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(7) = 28\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCreate a function which satisfies the pattern shown above.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pat(x)\r\n  y = sqrt(x)+2*x^2;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 10;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 3;\r\ny_correct = 16;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 7;\r\ny_correct = 28;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 11;\r\ny_correct = 40;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 20;\r\ny_correct = 67;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 99;\r\ny_correct = 304;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 12345;\r\ny_correct = 37042;\r\nassert(isequal(pat(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":290,"test_suite_updated_at":"2020-12-17T18:55:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-17T18:47:37.000Z","updated_at":"2026-03-20T14:58:29.000Z","published_at":"2020-12-17T18:55:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the pattern for the following sequence:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(1) = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(3) = 16\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(7) = 28\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a function which satisfies the pattern shown above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47255,"title":"Find Logic 8","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 191.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 95.8333px; transform-origin: 174px 95.8333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) =  3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 15\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 0;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 8;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 24\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":467,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-04T07:53:36.000Z","updated_at":"2026-02-14T07:11:40.000Z","published_at":"2020-11-04T07:53:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) =  3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 15\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45254,"title":"Tribonacci Sequence","description":"Generate the tribonacci sequence upto n","description_html":"\u003cp\u003eGenerate the tribonacci sequence upto n\u003c/p\u003e","function_template":"function t = tribonacci(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nn = 5;\r\ny_correct = [0,0,1,1,2];\r\nassert(isequal(tribonacci(n),y_correct))\r\n%%\r\nn = 11;\r\ny_correct = [0     0     1     1     2     4     7    13    24    44  81  ];\r\nassert(isequal(tribonacci(n),y_correct))\r\n%%\r\nn = 21;\r\ny_correct = [0\t0\t1\t1\t2\t4\t7\t13\t24\t44\t81\t149\t274\t504\t927\t1705\t3136\t5768\t10609\t19513\t35890];\r\nassert(isequal(tribonacci(n),y_correct))\r\n%%\r\nn = 30;\r\ny_correct =[ 0\t0\t1\t1\t2\t4\t7\t13\t24\t44\t81\t149\t274\t504\t927\t1705\t3136\t5768\t10609\t19513\t35890\t66012\t121415\t223317\t410744\t755476\t1389537\t2555757\t4700770\t8646064];\r\nassert(isequal(tribonacci(n),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":45,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-03T19:15:46.000Z","updated_at":"2025-06-14T03:37:34.000Z","published_at":"2020-01-03T19:19:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGenerate the tribonacci sequence upto n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60306,"title":"Add non-triangular numbers","description":"The nth triangular number is the sum of the first n positive integers. The sequence of triangular numbers starts 1, 3, 6, 10, 15, and 21. These numbers are involved in Cody Problems 5, 291, 44289, 44334, 44732, 55680, 55695, 55705, 55710, and 55715, for example. \r\nWrite a function to return the sum of the non-triangular numbers between the nth and (n+1)st triangular numbers. For example, if n = 3, then the function should return 7+8+9 = 24. Beware the banned functions.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377.658px 8px; transform-origin: 377.658px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe nth triangular number is the sum of the first n positive integers. The sequence of triangular numbers starts 1, 3, 6, 10, 15, and 21. These numbers are involved in Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/5\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e5\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/291\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e291\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44289\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44289\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44334\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44334\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44732\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44732\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55680\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55680\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55695\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55695\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55705\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55705\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55710\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55710\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.775px 8px; transform-origin: 16.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55715\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55715\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 8px; transform-origin: 44.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, for example. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 362.975px 8px; transform-origin: 362.975px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to return the sum of the non-triangular numbers between the nth and (n+1)st triangular numbers. For example, if n = 3, then the function should return 7+8+9 = 24. Beware the banned functions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = addNonTriangular(n)\r\n  y = sum(tril(n)+1:triu(n)-1);\r\nend","test_suite":"%%\r\nassert(isequal(addNonTriangular(1),2))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(2),9))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(3),24))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(4),50))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(44),44550))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(92),397854))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(267),9588504))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(389),29583450))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(461),49198842))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(556),86249222))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(632),126617724))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(709),178703450))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(878),339189399))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(913),381358274))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(1255),989903840))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(6534),139521237075))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(14342),1475229944979))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(78422),241154195453019))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(256347),8422831459859544))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(addNonTriangular(2429)/(3^10*347)),21560175))\r\n\r\n%%\r\ns = [0 1 4 9 6 5 6 9 4 1];\r\nn = randi(1000);\r\nm = n:n+2;\r\nd = num2str((2*arrayfun(@addNonTriangular,m)./m)')-'0';\r\nd1 = d(:,end)';\r\nassert(~isempty(strfind([s s],d1)))\r\n\r\n%%\r\nfiletext = fileread('addNonTriangular.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp') || contains(filetext,'sum') || contains(filetext,'trace')  || contains(filetext,'ones')  || contains(filetext,'eye'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-14T01:38:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-14T01:37:57.000Z","updated_at":"2026-03-04T14:14:54.000Z","published_at":"2024-05-14T01:38:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe nth triangular number is the sum of the first n positive integers. The sequence of triangular numbers starts 1, 3, 6, 10, 15, and 21. These numbers are involved in Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/5\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/291\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e291\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44289\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44289\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44334\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44334\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44732\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44732\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55680\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55680\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55695\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55695\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55705\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55705\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55710\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55710\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55715\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55715\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, for example. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to return the sum of the non-triangular numbers between the nth and (n+1)st triangular numbers. For example, if n = 3, then the function should return 7+8+9 = 24. Beware the banned functions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44543,"title":"Normie Function","description":"So, I built a function and gave it a name- _Normie_.\r\n*Find the nth term of Normie function:*\r\n_f(n)= 1*f(n-1)+ 2*f(n-3)+ 3_ , *when n\u003e3* and _0_ , *when n\u003c=3*.","description_html":"\u003cp\u003eSo, I built a function and gave it a name- \u003ci\u003eNormie\u003c/i\u003e. \u003cb\u003eFind the nth term of Normie function:\u003c/b\u003e \u003ci\u003ef(n)= 1*f(n-1)+ 2*f(n-3)+ 3\u003c/i\u003e , \u003cb\u003ewhen n\u0026gt;3\u003c/b\u003e and \u003ci\u003e0\u003c/i\u003e , \u003cb\u003ewhen n\u0026lt;=3\u003c/b\u003e.\u003c/p\u003e","function_template":"function y = nth_term(n)\r\n  y = n;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = 0;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 2;\r\ny_correct = 0;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 3;\r\ny_correct = 0;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 4;\r\ny_correct = 3;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 5;\r\ny_correct = 6;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 10;\r\ny_correct = 93;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 11;\r\ny_correct = 162;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 20;\r\ny_correct = 18753;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 35;\r\ny_correct = 51651090;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 50;\r\ny_correct = 142236278205;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 70;\r\ny_correct = 5490159117130629;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 75;\r\ny_correct = 76953534045721408;\r\nassert(isequal(nth_term(n),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":104442,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2018-03-28T11:14:13.000Z","rescore_all_solutions":false,"group_id":61,"created_at":"2018-03-21T19:10:33.000Z","updated_at":"2026-03-16T11:15:12.000Z","published_at":"2018-03-21T19:30:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo, I built a function and gave it a name-\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNormie\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFind the nth term of Normie function:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef(n)= 1*f(n-1)+ 2*f(n-3)+ 3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhen n\u0026gt;3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhen n\u0026lt;=3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60271,"title":"Hofstadter G sequence","description":"The Hofstadter G sequence is defined as follows:\r\n\r\nThe first elements of the sequence are 0, 1, 1, 2, 3, 3, 4, 4, 5, 6.\r\nWrite a function to compute  for a given n.\r\nSee https://oeis.org/A005206","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 171.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343.5px 85.85px; transform-origin: 343.5px 85.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.5px; text-align: left; transform-origin: 320.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Hofstadter G sequence is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 49.4px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 24.7px; text-align: left; transform-origin: 320.5px 24.7px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-19px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"110\" height=\"49.5\" style=\"width: 110px; height: 49.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.9px; text-align: left; transform-origin: 320.5px 10.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first elements of the sequence are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e0, 1, 1, 2, 3, 3, 4, 4, 5, 6\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 11.25px; text-align: left; transform-origin: 320.5px 11.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003efor a given\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.5px; text-align: left; transform-origin: 320.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSee \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A005206\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://oeis.org/A005206\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function G = G_sequence(n)\r\n\r\nend","test_suite":"all_glo = [0, 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 30, 31, 32, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 43, 44, 45, 45, 46, 46, 47, 48, 48, 49, 50, 50, 51, 51, 52, 53, 53, 54, 55, 55, 56, 56, 57, 58, 58, 59, 59, 60, 61, 61, 62, 63, 63, 64, 64, 65, 66, 66, 67, 67, 68, 69, 69, 70, 71, 71, 72, 72, 73, 74, 74, 75, 76, 76, 77, 77, 78, 79, 79, 80, 80, 81, 82, 82, 83, 84, 84, 85, 85, 86, 87, 87, 88, 88, 89, 90, 90, 91, 92, 92, 93, 93, 94, 95, 95, 96, 97, 97, 98, 98, 99, 100, 100, 101, 101, 102, 103, 103, 104, 105, 105, 106, 106, 107, 108, 108, 109, 110, 110, 111, 111, 112, 113, 113, 114, 114, 115, 116, 116, 117, 118, 118, 119, 119, 120, 121, 121, 122, 122, 123, 124, 124, 125, 126, 126, 127, 127, 128, 129, 129, 130, 131, 131, 132, 132, 133, 134, 134, 135, 135, 136, 137, 137, 138, 139, 139, 140, 140, 141, 142, 142];\r\nn = randi([90,numel(all_glo)]) \r\ny_correct = all_glo(n+1)\r\n\r\n%%\r\n% Only for this random test, n and y_correct are displayed but their definition is hidden.\r\nn\r\ny_obtained = G_sequence(n)\r\ny_correct\r\nassert(isequal(y_obtained,y_correct));\r\n\r\n\r\n%%\r\nn = 76\r\ny_obtained = G_sequence(n)\r\ny_correct = 47\r\nassert(isequal(y_obtained,y_correct));\r\n\r\n%%\r\nyy_correct = [0, 1, 1, 2, 3, 3, 4, 4, 5, 6];\r\nfor n = 0:numel(yy_correct)-1\r\n    y_obtained = G_sequence(n);\r\n    y_correct = yy_correct(n+1);\r\n    assert(isequal(y_obtained,y_correct));\r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-11T17:00:10.000Z","updated_at":"2026-03-02T09:18:08.000Z","published_at":"2024-05-11T17:00:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Hofstadter G sequence is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$$\\\\begin{cases}\\nG_0 = 0\\\\\\\\\\nG_n = n-G_{G_{n-1}}\\n\\\\end{cases}$$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first elements of the sequence are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0, 1, 1, 2, 3, 3, 4, 4, 5, 6\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003efor a given\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A005206\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://oeis.org/A005206\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42835,"title":"Return the sequence element II","description":"Given positive integers x and n, return a positive integer, y, which is the nth term in the \u003chttps://en.wikipedia.org/wiki/Juggler_sequence Juggler sequence\u003e beginning with x.\r\n\r\nThe Juggler sequence is defined by:\r\n\r\na(i+1) = floor(a(i)^0.5) , for even a(i).\r\n\r\na(i+1) = floor(a(i)^1.5) , for odd a(i).\r\n\r\nFor the purpose of this problem, the first element in the sequence is a(1) = x.\r\n\r\nExample:\r\n\r\nx = 3\r\n\r\nn = 5\r\n\r\ny = 6","description_html":"\u003cp\u003eGiven positive integers x and n, return a positive integer, y, which is the nth term in the \u003ca href = \"https://en.wikipedia.org/wiki/Juggler_sequence\"\u003eJuggler sequence\u003c/a\u003e beginning with x.\u003c/p\u003e\u003cp\u003eThe Juggler sequence is defined by:\u003c/p\u003e\u003cp\u003ea(i+1) = floor(a(i)^0.5) , for even a(i).\u003c/p\u003e\u003cp\u003ea(i+1) = floor(a(i)^1.5) , for odd a(i).\u003c/p\u003e\u003cp\u003eFor the purpose of this problem, the first element in the sequence is a(1) = x.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003ex = 3\u003c/p\u003e\u003cp\u003en = 5\u003c/p\u003e\u003cp\u003ey = 6\u003c/p\u003e","function_template":"function y = juggler(x,n)\r\n  y = x + n;\r\nend","test_suite":"%%\r\nx = 3;\r\nn = 5;\r\ny_correct = 6;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 33;\r\nn = 3;\r\ny_correct = 2598;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 45;\r\nn = 4;\r\ny_correct = 72;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 163;\r\nn = 23;\r\ny_correct = 333;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 37;\r\nn = 13;\r\ny_correct = 34276462;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 37;\r\nn = 18;\r\ny_correct = 1;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 37;\r\nn = 99;\r\ny_correct = 1;\r\nassert(isequal(juggler(x,n),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":45,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-27T19:07:54.000Z","updated_at":"2026-03-05T12:02:09.000Z","published_at":"2016-04-27T19:07:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven positive integers x and n, return a positive integer, y, which is the nth term in the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Juggler_sequence\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eJuggler sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e beginning with x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Juggler sequence is defined by:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(i+1) = floor(a(i)^0.5) , for even a(i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(i+1) = floor(a(i)^1.5) , for odd a(i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor the purpose of this problem, the first element in the sequence is a(1) = x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45224,"title":"Wythoff Sequence","description":"\r\nFind the lower Wythoff sequence up to n.\r\n\r\nFor more information, \u003chttps://oeis.org/A000201\u003e","description_html":"\u003cp\u003eFind the lower Wythoff sequence up to n.\u003c/p\u003e\u003cp\u003eFor more information, \u003ca href = \"https://oeis.org/A000201\"\u003ehttps://oeis.org/A000201\u003c/a\u003e\u003c/p\u003e","function_template":"function y=wythoff(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = 1;\r\nassert(isequal(wythoff(n),y_correct))\r\n%%\r\nn = 10;\r\ny_correct = [1,3,4,6,8,9,11,12,14,16];\r\nassert(isequal(wythoff(n),y_correct))\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-04T12:02:31.000Z","updated_at":"2026-03-16T11:21:35.000Z","published_at":"2019-12-04T12:20:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the lower Wythoff sequence up to n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor more information,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A000201\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://oeis.org/A000201\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":3011,"title":"Self-similarity 2 - Every third term","description":"Self-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003chttps://oeis.org/selfsimilar.html OEIS page\u003e for more information.\r\n\r\nIn this problem, you are to check if the sequence is self-similar by every third term. The problem set assumes that you start with the first element and then take every third element thereafter of the original sequence, and compare that result to the first third of the original sequence. The function should return true if the extracted sequence is equal to the first third of the original sequence.\r\n\r\nFor example,\r\n\r\n* seq_original_set = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4]\r\n* seq_every_third = [0, , , 1, , , 2, , , 1, , , 2, , ,] (extra commas are instructional and should not be in the every-other series) \r\n* seq_orig_first_third = [0, 1, 2, 1, 2]\r\n\r\nSince seq_every_third = seq_orig_first_third, the set is self-similar.\r\n\r\nThis problem is related to \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term Problem 3010\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms Problem 3012\u003e.","description_html":"\u003cp\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003ca href = \"https://oeis.org/selfsimilar.html\"\u003eOEIS page\u003c/a\u003e for more information.\u003c/p\u003e\u003cp\u003eIn this problem, you are to check if the sequence is self-similar by every third term. The problem set assumes that you start with the first element and then take every third element thereafter of the original sequence, and compare that result to the first third of the original sequence. The function should return true if the extracted sequence is equal to the first third of the original sequence.\u003c/p\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cul\u003e\u003cli\u003eseq_original_set = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4]\u003c/li\u003e\u003cli\u003eseq_every_third = [0, , , 1, , , 2, , , 1, , , 2, , ,] (extra commas are instructional and should not be in the every-other series)\u003c/li\u003e\u003cli\u003eseq_orig_first_third = [0, 1, 2, 1, 2]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eSince seq_every_third = seq_orig_first_third, the set is self-similar.\u003c/p\u003e\u003cp\u003eThis problem is related to \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term\"\u003eProblem 3010\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms\"\u003eProblem 3012\u003c/a\u003e.\u003c/p\u003e","function_template":"function [tf] = self_similarity_2(seq)\r\n\r\ntf = 0;\r\n\r\nend\r\n","test_suite":"%%\r\nseq = [1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 2, 0, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 3, 3, 0, 0, 2, 1, 4, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 4, 0, 1, 2, 0, 3, 0, 4, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 3, 2, 3, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 4, 7, 2, 5, 9, 1, 10, 19, 4, 13, 22, 7, 16, 25, 2, 11, 20, 5, 14, 23, 8, 17, 26, 1, 28, 55, 10, 37, 64, 19, 46, 73, 4, 31, 58, 13, 40, 67, 22, 49, 76, 7, 34, 61, 16, 43, 70, 25, 52, 79, 2, 29, 56, 11, 38, 65, 20, 47, 74, 5, 32, 59, 14, 41, 68, 23, 50, 77, 8, 35, 62, 17, 44, 71];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 3, 2, 2, 3, 1, 1, 2, 1, 1, 3, 2, 2, 3, 0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3, 4, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 11, 12, 2, 12, 22, 1, 11, 12, 11, 12, 112, 12, 112, 122, 2, 12, 22, 12, 112, 122, 22, 122, 222, 1, 11, 12, 11, 111, 112, 12, 112, 122, 11, 111, 112, 111, 1111, 1112, 112, 1112, 1122, 12, 112, 122, 112, 1112, 1122, 122, 1122, 1222, 2, 12, 22, 12, 112];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 4, 1, 2, 5, 4, 5, 8, 1, 2, 5, 1, 3, 6, 5, 6, 9, 4, 5, 8, 5, 6, 9, 8, 9, 12, 1, 2, 5, 2, 3, 6, 5, 6, 9, 2, 3, 6, 3, 4, 7, 6, 7, 10, 5, 6, 9, 6, 7, 10, 9, 10, 13, 4, 5, 8, 5, 6, 9, 8, 9, 12, 5, 6, 9, 6, 7];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 12, 36, 12, 84, 72, 36, 96, 180, 12, 216, 180, 84, 168, 288, 72, 372, 216, 36, 240, 504, 96, 432, 288, 180, 372, 504, 12, 672, 360, 216, 384, 756, 144, 648, 576, 84, 456, 720, 168, 1080, 504, 288, 528, 1008, 72, 864, 576, 372, 684, 1116, 216, 1176, 648, 36];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 2, 0, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 3, 3, 0, 0, 2, 1, 4, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 4, 0, 1, 2, 0, 3, 0, 4, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 3, 2, 3, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 1, 0, 1, 2, 1, 1, 2, 0, 0, 1, 0, 0, 3, 2, 2, 3, 1, 1, 2, 1, 1, 3, 2, 2, 3, 0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3, 4, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 4, 6, 3, 6, 9, 2, 4, 6, 4, 8, 12, 6, 12, 18, 3, 6, 9, 6, 12, 18, 9, 18, 27, 2, 4, 6, 4, 8, 12, 6, 12, 18, 4, 8, 12, 8, 16, 24, 12, 24, 36, 6, 12, 18, 12, 24, 36, 18, 36, 54, 3, 6, 9, 6, 12, 18, 9, 18, 27, 6, 12, 18, 12, 24, 36, 18, 36, 54, 9, 18, 27, 18, 36, 54, 27, 54];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 4, 1, 2, 5, 4, 5, 8, 1, 2, 5, 2, 3, 6, 5, 6, 9, 4, 5, 8, 5, 6, 9, 8, 9, 12, 1, 2, 5, 2, 3, 6, 5, 6, 9, 2, 3, 6, 3, 4, 7, 6, 7, 10, 5, 6, 9, 6, 7, 10, 9, 10, 13, 4, 5, 8, 5, 6, 9, 8, 9, 12, 5, 6, 9, 6, 7];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 12, 36, 12, 84, 72, 36, 96, 180, 12, 216, 144, 84, 168, 288, 72, 372, 216, 36, 240, 504, 96, 432, 288, 180, 372, 504, 12, 672, 360, 216, 384, 756, 144, 648, 576, 84, 456, 720, 168, 1080, 504, 288, 528, 1008, 72, 864, 576, 372, 684, 1116, 216, 1176, 648, 36];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 2, 1, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 0, 1, 2, 1, 2, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 3, 1, 3, 1, 2, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2, 2, 3, 1, 3, 1, 2, 1, 2, 3, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 4, 7, 2, 5, 8, 1, 10, 19, 4, 13, 22, 7, 16, 25, 2, 11, 20, 5, 14, 23, 8, 17, 26, 1, 28, 55, 10, 37, 64, 19, 46, 73, 4, 31, 58, 13, 40, 67, 22, 49, 76, 7, 34, 61, 16, 43, 70, 25, 52, 79, 2, 29, 56, 11, 38, 65, 20, 47, 74, 5, 32, 59, 14, 41, 68, 23, 50, 77, 8, 35, 62, 17, 44, 71];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 2, 1, 2, 3, 2, 3, 4, 1, 3, 5, 2, 4, 6, 3, 5, 7, 2, 4, 6, 3, 5, 7, 4, 6, 8, 1, 2, 3, 3, 4, 5, 5, 6, 7, 2, 3, 4, 4, 5, 6, 6, 7, 8, 3, 4, 5, 5, 6, 7, 7, 8, 9, 2, 3, 4, 4, 5, 6, 6, 7, 8, 3, 4, 5, 5, 6, 7, 7, 8, 9, 4, 5, 6, 6, 7, 8, 8, 9, 10, 1, 3, 5, 2, 4, 6, 3, 5, 7, 3, 5, 7, 4, 6, 8, 5, 7, 9, 5, 7, 9];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 1, 1, 3, 1, 1, 2, 3, 2, 1, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [\t1, 2, 0, 2, 6, 0, 0, 4, 0, 2, 0, 0, 6, 4, 0, 0, 6, 0, 0, 4, 0, 4, 0, 0, 0, 2, 0, 2, 12, 0, 0, 4, 0, 0, 0, 0, 6, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 6, 6, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 6, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 12, 0, 0, 4, 0, 2, 0, 0, 12, 0, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 0, 6, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 3, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 6, 0, 0, 6, 4, 2, 4, 12, 6, 4, 8, 0, 10, 0, 0, 16, 8, 6, 4, 12, 4, 14, 8, 2, 34, 12, 4, 16, 40, 12, 12, 48, 6, 28, 8, 4, 44, 24, 8, 16, 44, 0, 12, 24, 10, 58, 16, 0, 28, 36, 0, 24, 100, 16, 16, 48, 8, 28, 16, 6, 62];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 6, 0, 0, 4, 0, 2, 0, 0, 6, 6, 4, 0, 10, 12, 0, 4, 8, 4, 4, 0, 0, 14, 8, 2, 12, 12, 0, 4, 8, 0, 8, 0, 6, 4, 4, 6, 8, 24, 4, 16, 8, 0, 8, 0, 10, 18, 8, 12, 34, 12, 0, 24, 44, 4, 8, 24, 8, 28, 12, 4, 46, 48, 4, 28, 36, 0, 16];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 4, 5, 2, 5, 8, 1, 3, 5, 4, 13, 14, 5, 14, 17, 2, 5, 8, 5, 14, 17, 8, 17, 26, 1, 4, 5, 4, 13, 14, 5, 14, 17, 4, 13, 14, 13, 40, 41, 14, 41, 44, 5, 14, 17, 14, 41, 44, 17, 44, 53, 2, 5, 8, 5, 14, 17, 8, 17, 26, 5, 14, 17, 14, 41, 44, 17, 44, 53, 8, 17, 26, 17, 44, 53, 26, 53, 80];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 4, 20, 24, 4, 32, 52, 4, 24, 48, 20, 56, 32, 24, 116, 72, 4, 80, 120, 32, 48, 96, 52, 124, 56, 4, 160, 120, 24, 128, 244, 48, 72, 192, 20, 152, 80, 56, 312, 168, 32, 176, 240, 24, 96, 192, 116, 228, 124, 72, 280, 216, 4, 288, 416, 80, 120, 240, 120, 248, 128, 32, 500];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 4, 6, 3, 6, 9, 2, 4, 6, 4, 8, 16, 6, 12, 18, 3, 6, 9, 6, 12, 18, 9, 18, 27, 2, 4, 6, 4, 8, 12, 6, 12, 18, 4, 8, 12, 8, 16, 24, 12, 24, 36, 6, 12, 18, 12, 24, 36, 18, 36, 54, 3, 6, 9, 6, 12, 18, 9, 18, 27, 6, 12, 18, 12, 24, 36, 18, 36, 54, 9, 18, 27, 18, 36, 54, 27, 54];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 4, 5, 2, 5, 8, 1, 4, 5, 4, 13, 14, 5, 14, 17, 2, 5, 8, 5, 14, 17, 8, 17, 26, 1, 4, 5, 4, 13, 14, 5, 14, 17, 4, 13, 14, 13, 40, 41, 14, 41, 44, 5, 14, 17, 14, 41, 44, 17, 44, 53, 2, 5, 8, 5, 14, 17, 8, 17, 26, 5, 14, 17, 14, 41, 44, 17, 44, 53, 8, 17, 26, 17, 44, 53, 26, 53, 80];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 6, 0, 0, 4, 0, 2, 0, 0, 6, 8, 4, 2, 10, 12, 0, 4, 8, 4, 4, 0, 0, 14, 8, 2, 12, 12, 0, 4, 8, 0, 8, 0, 6, 4, 4, 6, 8, 24, 4, 16, 8, 0, 8, 0, 10, 18, 8, 12, 34, 12, 0, 24, 44, 4, 8, 24, 8, 28, 12, 4, 46, 48, 4, 28, 36, 0, 16];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 4, 20, 24, 4, 32, 52, 4, 24, 48, 40, 56, 32, 64, 116, 72, 4, 80, 120, 32, 48, 96, 52, 124, 56, 4, 160, 120, 24, 128, 244, 48, 72, 192, 20, 152, 80, 56, 312, 168, 32, 176, 240, 24, 96, 192, 116, 228, 124, 72, 280, 216, 4, 288, 416, 80, 120, 240, 120, 248, 128, 32, 500];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 11, 12, 2, 12, 22, 1, 11, 12, 11, 111, 112, 12, 112, 122, 2, 12, 22, 12, 112, 122, 22, 122, 222, 1, 11, 12, 11, 111, 112, 12, 112, 122, 11, 111, 112, 111, 1111, 1112, 112, 1112, 1122, 12, 112, 122, 112, 1112, 1122, 122, 1122, 1222, 2, 12, 22, 12, 112];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 4, 4, 12, 4, 4, 4, 4, 12, 4, 4, 12, 4, 12, 4, 12, 4, 4, 12, 4, 4, 4, 4, 20, 12, 4, 4, 12, 12, 4, 4, 4, 12, 12, 4, 12, 4, 12, 12, 12, 4, 4, 4, 12, 4, 4, 4, 4, 20, 12, 12, 12, 4, 12, 4, 4, 12, 4, 12, 12, 4, 4, 4, 36, 4, 4, 12, 4, 12, 4, 4, 12, 12, 20, 4, 4, 12, 4, 12, 4, 12, 4, 4, 36];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 4, 3, 4, 3, 1, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 3, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 2, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2, 2, 3, 1, 3, 1, 2, 1, 2, 3, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 2, 1, 2, 3, 2, 3, 4, 1, 2, 5, 2, 4, 5, 3, 5, 7, 2, 4, 6, 3, 5, 7, 4, 6, 8, 1, 2, 3, 3, 4, 5, 5, 6, 7, 2, 3, 4, 4, 5, 6, 6, 7, 8, 3, 4, 5, 5, 6, 7, 7, 8, 9, 2, 3, 4, 4, 5, 6, 6, 7, 8, 3, 4, 5, 5, 6, 7, 7, 8, 9, 4, 5, 6, 6, 7, 8, 8, 9, 10, 1, 3, 5, 2, 4, 6, 3, 5, 7, 3, 5, 7, 4, 6, 8, 5, 7, 9, 5, 7, 9];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 4, 4, 12, 4, 4, 8, 4, 12, 4, 4, 12, 4, 12, 4, 12, 4, 4, 12, 4, 4, 4, 4, 20, 12, 4, 4, 12, 12, 4, 4, 4, 12, 12, 4, 12, 4, 12, 12, 12, 4, 4, 4, 12, 4, 4, 4, 4, 20, 12, 12, 12, 4, 12, 4, 4, 12, 4, 12, 12, 4, 4, 4, 36, 4, 4, 12, 4, 12, 4, 4, 12, 12, 20, 4, 4, 12, 4, 12, 4, 12, 4, 4, 36];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [\t1, 2, 0, 2, 6, 0, 1, 4, 0, 2, 0, 0, 6, 4, 1, 0, 6, 0, 0, 4, 0, 4, 0, 0, 0, 2, 0, 2, 12, 0, 0, 4, 0, 0, 0, 0, 6, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 6, 6, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 6, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 12, 0, 0, 4, 0, 2, 0, 0, 12, 0, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 0, 6, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 6, 0, 2, 6, 4, 2, 4, 12, 6, 4, 8, 2, 10, 0, 0, 16, 8, 6, 4, 12, 4, 14, 8, 2, 34, 12, 4, 16, 40, 12, 12, 48, 6, 28, 8, 4, 44, 24, 8, 16, 44, 0, 12, 24, 10, 58, 16, 0, 28, 36, 0, 24, 100, 16, 16, 48, 8, 28, 16, 6, 62];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 2, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 0, 1, 2, 1, 2, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":66,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":30,"created_at":"2015-02-13T04:22:00.000Z","updated_at":"2026-03-11T15:38:45.000Z","published_at":"2015-02-13T04:22:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/selfsimilar.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOEIS page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more information.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, you are to check if the sequence is self-similar by every third term. The problem set assumes that you start with the first element and then take every third element thereafter of the original sequence, and compare that result to the first third of the original sequence. The function should return true if the extracted sequence is equal to the first third of the original sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_original_set = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_every_third = [0, , , 1, , , 2, , , 1, , , 2, , ,] (extra commas are instructional and should not be in the every-other series)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_orig_first_third = [0, 1, 2, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince seq_every_third = seq_orig_first_third, the set is self-similar.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is related to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3010\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3012\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":59791,"title":"Complete a geometric sequence","description":"In Cody Problem 59786 minnolina asks us to find the integer that completes a randomly sorted arithmetic sequence with one missing element. This problem is similar, but it deals with geometric sequences. For example, in the list [4 8 32 128 16 2], the common ratio is 2, and the missing element is 64. \r\nWrite a function to find the missing element in a randomly sorted geometric sequence. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59786\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 59786\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 299.9px 8px; transform-origin: 299.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e minnolina asks us to find the integer that completes a randomly sorted arithmetic sequence with one missing element. This problem is similar, but it deals with geometric sequences. For example, in the list \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46.2px 8px; transform-origin: 46.2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[4 8 32 128 16 2]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 171.133px 8px; transform-origin: 171.133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the common ratio is 2, and the missing element is 64. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 267.875px 8px; transform-origin: 267.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find the missing element in a randomly sorted geometric sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = completeGeomSeq(x)\r\n   y = mean(x);\r\nend","test_suite":"%%\r\nx = [4 8 32 128 16 2];\r\ny = completeGeomSeq(x);\r\ny_correct = 64;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nx = [19683 2187 9 3 243 27 81 6561];\r\ny = completeGeomSeq(x);\r\ny_correct = 729;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nx = [256 67108864 262144 1048576 16384 64 65536 1024 4096 1073741824 16777216 4194304];\r\ny = completeGeomSeq(x);\r\ny_correct = 268435456;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nx = [390625 125 78125 15625 625 3125 9765625];\r\ny = completeGeomSeq(x);\r\ny_correct = 1953125;\r\nassert(isequal(y,y_correct))\r\n\r\n%% \r\nfor k = 1:randi(8)\r\n    b = 1+randi(12);\r\n    e1 = randi(4);\r\n    en = e1+2+randi(6);\r\n    x1 = b.^(e1:en);\r\n    indx = 1+randi(length(x1)-2);\r\n    y_correct = x1(indx);\r\n    x1(indx) = [];\r\n    x = x1(randperm(length(x1)));\r\n    y = completeGeomSeq(x);\r\n    assert(isequal(y,y_correct))\r\nend","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-03-31T23:55:34.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-31T23:55:30.000Z","updated_at":"2026-03-02T14:55:52.000Z","published_at":"2024-03-31T23:55:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59786\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 59786\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e minnolina asks us to find the integer that completes a randomly sorted arithmetic sequence with one missing element. This problem is similar, but it deals with geometric sequences. For example, in the list \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[4 8 32 128 16 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the common ratio is 2, and the missing element is 64. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find the missing element in a randomly sorted geometric sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47265,"title":"Find Logic 10","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 191.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 95.8333px; transform-origin: 174px 95.8333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 120\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 60\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 20\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 120;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 60;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx=5;\r\ny_correct = 1;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":415,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-04T08:47:44.000Z","updated_at":"2026-02-14T07:05:44.000Z","published_at":"2020-11-04T08:47:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 60\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 20\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57869,"title":"Identify de Polignac numbers","description":"The numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, , and . The numbers 127 and 331, which are examples of de Polignac numbers, cannot be written in this way.\r\nWrite a function that determines whether an odd number is a de Polignac number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 297.55px 8px; transform-origin: 297.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"125 = 109+2^4\" style=\"width: 96px; height: 19px;\" width=\"96\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"329 = 73+2^8\" style=\"width: 88.5px; height: 19px;\" width=\"88.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 320.392px 8px; transform-origin: 320.392px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The numbers 127 and 331, which are examples of de Polignac numbers, cannot be written in this way.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 255.042px 8px; transform-origin: 255.042px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that determines whether an odd number is a de Polignac number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isdePolignac(n)\r\n  tf = isequal(n,p+2^k);\r\nend","test_suite":"%%\r\nassert(isdePolignac(1))\r\n\r\n%%\r\nassert(~isdePolignac(17))\r\n\r\n%%\r\nassert(~isdePolignac(75))\r\n\r\n%%\r\nassert(isdePolignac(127))\r\n\r\n%%\r\nassert(isdePolignac(331))\r\n\r\n%%\r\nassert(~isdePolignac(531))\r\n\r\n%%\r\nassert(isdePolignac(905))\r\n\r\n%%\r\nassert(isdePolignac(1619))\r\n\r\n%%\r\nassert(~isdePolignac(2261))\r\n\r\n%%\r\nassert(isdePolignac(7535))\r\n\r\n%%\r\nassert(~isdePolignac(10413))\r\n\r\n%%\r\nassert(isdePolignac(21453))\r\n\r\n%%\r\nassert(isdePolignac(45233))\r\n\r\n%%\r\nassert(~isdePolignac(70999))\r\n\r\n%%\r\nassert(~isdePolignac(96415))\r\n\r\n%%\r\nassert(~isdePolignac(121399))\r\n\r\n%%\r\nassert(isdePolignac(148243))\r\n\r\n%%\r\nassert(isdePolignac(172841))\r\n\r\n%%\r\nassert(isdePolignac(201599))\r\n\r\n%%\r\nassert(isdePolignac(227107))\r\n\r\n%%\r\nassert(isdePolignac(253151))\r\n\r\n%%\r\nassert(~isdePolignac(267267))\r\n\r\n%%\r\nassert(~isdePolignac(271271))\r\n\r\n%%\r\nassert(isdePolignac(273421))\r\n\r\n%%\r\nassert(isdePolignac(542459))\r\n\r\n%%\r\nassert(isdePolignac(2000039))\r\n\r\n%%\r\nassert(~isdePolignac(123456789))\r\n\r\n%%\r\nassert(isdePolignac(123456791))\r\n\r\n%%\r\nassert(isequal(bin2dec(num2str(arrayfun(@isdePolignac,5893:2:5933)')'),288))\r\n\r\n%%\r\nassert(isequal(bin2dec(num2str(arrayfun(@isdePolignac,21671:10:21791)')'),4624))\r\n\r\n%%\r\nfiletext = fileread('isdePolignac.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-29T05:27:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-29T05:27:08.000Z","updated_at":"2025-12-25T08:44:06.000Z","published_at":"2023-03-29T05:27:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"125 = 109+2^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e125 = 109+2^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"329 = 73+2^8\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e329 = 73+2^8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The numbers 127 and 331, which are examples of de Polignac numbers, cannot be written in this way.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that determines whether an odd number is a de Polignac number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47239,"title":"Find Logic 5","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 191.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 95.8333px; transform-origin: 174px 95.8333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the logic\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 14\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which returns 'x' th term of logic\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 2;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 20;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 44;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":67,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-03T16:42:59.000Z","updated_at":"2026-03-16T11:57:14.000Z","published_at":"2020-11-03T16:42:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the logic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which returns 'x' th term of logic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60276,"title":"Hofstadter H sequence","description":"The Hofstadter H sequence is defined as follows:\r\n\r\nThe first elements of the sequence are 0, 1, 1, 2, 3, 4, 4, 5, 5, 6.\r\nWrite a function to compute  for a given n.\r\nSee https://oeis.org/A005374","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 175.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 87.75px; transform-origin: 407px 87.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Hofstadter H sequence is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 54px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 27px; text-align: left; transform-origin: 384px 27px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-21px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"118\" height=\"54\" style=\"width: 118px; height: 54px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first elements of the sequence are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e0, 1, 1, 2, 3, 4, 4, 5, 5, 6\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003efor a given\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSee \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A005374\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://oeis.org/A005374\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function h = H_sequence(n)\r\n\r\nend","test_suite":"all_glo = [0, 1, 1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 13, 13, 14, 14, 15, 16, 17, 17, 18, 18, 19, 20, 20, 21, 22, 23, 23, 24, 24, 25, 26, 26, 27, 28, 29, 29, 30, 31, 32, 32, 33, 33, 34, 35, 35, 36, 37, 38, 38, 39, 40, 41, 41, 42, 42, 43, 44, 45, 45, 46, 46, 47, 48, 48, 49, 50, 51, 51, 52, 53, 54, 54, 55, 55, 56, 57, 58, 58, 59, 59, 60, 61, 61, 62, 63, 64, 64, 65, 65, 66, 67, 67, 68, 69, 70, 70, 71, 72, 73, 73, 74, 74, 75, 76, 77, 77, 78, 78, 79, 80, 80, 81, 82, 83, 83, 84, 84, 85, 86, 86, 87, 88, 89, 89, 90, 91, 92, 92, 93, 93, 94, 95, 95, 96, 97, 98, 98, 99, 100, 101, 101, 102, 102, 103, 104, 105, 105, 106, 106, 107, 108, 108, 109, 110, 111, 111, 112, 112, 113, 114, 114, 115, 116, 117, 117, 118, 119, 120, 120, 121, 121, 122, 123, 123, 124, 125, 126, 126, 127, 128, 129, 129, 130, 130, 131, 132, 133, 133, 134, 134, 135, 136, 136, 137, 138, 139, 139, 140, 141, 142, 142, 143, 143, 144, 145, 146, 146, 147, 147, 148, 149, 149, 150, 151, 152, 152, 153, 153, 154, 155, 155, 156, 157];\r\nn = randi([90,numel(all_glo)]) \r\ny_correct = all_glo(n+1)\r\n\r\n%%\r\n% Only for this random test, n and y_correct are displayed but their definition is hidden.\r\nn\r\ny_obtained = H_sequence(n)\r\ny_correct\r\nassert(isequal(y_obtained,y_correct));\r\n\r\n\r\n%%\r\nn = 73\r\ny_obtained = H_sequence(n)\r\ny_correct = 50\r\nassert(isequal(y_obtained,y_correct));\r\n\r\n%%\r\nyy_correct = [0,1,1,2,3,4,4,5,5,6,7,7,8,9,10,10,11,12,13,13,14];\r\nfor n = 0:numel(yy_correct)-1\r\n    y_obtained = H_sequence(n);\r\n    y_correct = yy_correct(n+1);\r\n    assert(isequal(y_obtained,y_correct));\r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":208445,"edited_by":208445,"edited_at":"2024-06-04T13:10:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2024-05-11T17:10:59.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-11T17:04:48.000Z","updated_at":"2026-01-27T21:29:53.000Z","published_at":"2024-05-11T17:10:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Hofstadter H sequence is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$$\\\\begin{cases}\\nH_0 = 0\\\\\\\\\\nH_n = n-H_{H_{H_{n-1}}}\\n\\\\end{cases}$$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first elements of the sequence are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0, 1, 1, 2, 3, 4, 4, 5, 5, 6\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003efor a given\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A005374\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://oeis.org/A005374\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50953,"title":"Round up to π","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 191.35px 7.91667px; transform-origin: 191.35px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo commemorate Pi Day (March 14 in the U.S.), compute the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117.85px 7.91667px; transform-origin: 117.85px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term in a sequence by starting with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.2333px 7.91667px; transform-origin: 62.2333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, rounding up to the next multiple of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n-1\" style=\"width: 35px; height: 18px;\" width=\"35\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.242px 7.91667px; transform-origin: 111.242px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, rounding up to the next multiple of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n-2\" style=\"width: 35px; height: 18px;\" width=\"35\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 171.908px 7.91667px; transform-origin: 171.908px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and so on to rounding up to the next multiple of 1. For example, with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 244.467px 7.91667px; transform-origin: 244.467px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 8, you would get 14, 18, 20, 20, 21, 22, and—the element in the sequence—\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"f(n)\" style=\"width: 32.5px; height: 19px;\" width=\"32.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.6417px 7.91667px; transform-origin: 19.6417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 22. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.325px 7.91667px; transform-origin: 96.325px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEEAAAAmCAYAAACbBvanAAACiklEQVRoge2Zb5GDMBDFfx5wUAM1gIIqqAMc1EEtVEMlnAcsoKEWuA/JG/bugGxC4MvxZjod2slms/v2X4ATJ06cOLEbLkCbuaYBXvG7lg7PivLcuAID8EU40AfoHOuauOZaWZ8W6DnQEC0wAu/43MXnT0KJhqBoLnO8uEf5u6MhHPZDoCHAjWCEr8TaN4G2e+J1wB48+MkCL+6kmVIDctJebIO4wUg4VA4GggGPwDPutwvuBAOMTKGQs+6opHWJ+932EP6OwnOt3JPOF7XRkx+yi+gINH4whcJgfutY97C8khMKV4IXrScbAqMe+Dz8jPtWgQ77YgqFt/k9lRsUCqlE1RHYMpqPZN+YHKBPyhDefbOgqpArWOu8zVHPz57jTmBey1SKR9JlUL2Mp4FzQ/kgt8zJu14MTGxr47P208E8jriSH4ZJiI65CS7HCMof8qAYIIhVXkeU9DMu5XK7sRwj2BI88JfKYqP3YCVOW4SNxdzam2MEHXJJecsSD6oaQeWmpOHJMYJC7sPfRGrzgadRKynNq9BBSiY0GTBlPHvI14ocb6MmedWMsKZcChqzU9ncsm2unKp0Kiel2KAQrtInqNSUDE12fSqOdcg5T9vE3OK7mFElqTKvyJO5Q5PFwDqLGrPHHH1/69CTdkhPxQsWtctbRtMnIdktwZbGOfra/z2sklFLmDuL37FYAtF5SamWaRZZggY5Dxs7Kl7gWJpuvRh9ctw4PddoFUM0rBFbDUG5ahRdwIMN+updgLWgOrha46iu6UsTrEe+vQDOhh2VG6bSVtIbrOFGCIvaV226zt8UtrKiKJsqa1v3qmmIhsDaKi90LoRw6NiPskJNJjSV5Z04ceLE/8Q372/pj3B4BJgAAAAASUVORK5CYII=\" alt=\"f(n)\" style=\"width: 32.5px; height: 19px;\" width=\"32.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.55px 7.91667px; transform-origin: 15.55px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.517px 7.91667px; transform-origin: 122.517px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term in this sequence. Also compute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n^2/f(n)\" style=\"width: 52.5px; height: 20px;\" width=\"52.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.8417px 7.91667px; transform-origin: 68.8417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and notice its limit as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.1083px 7.91667px; transform-origin: 17.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e gets large. For more on this limit, see \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathpages.com/home/kmath001/kmath001.htm\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003ethis page\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.2167px 7.91667px; transform-origin: 48.2167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by K.S. Brown.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [a,y] = roundUpToPi(n)\r\n  a = f(n);\r\n  y = n^2/a;\r\nend","test_suite":"%%\r\nn = 1;\r\na_correct = 1;\r\ny_correct = 1;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 2;\r\na_correct = 2;\r\ny_correct = 2;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 8;\r\na_correct = 22;\r\ny_correct = 2.909090909090909;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 31;\r\na_correct = 322;\r\ny_correct = 2.984472049689441;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 314;\r\na_correct = 31422;\r\ny_correct = 3.137801540322067;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 3141;\r\na_correct = 3143652;\r\ny_correct = 3.138350237240;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 31415;\r\na_correct = 314162898;\r\ny_correct = 3.141371025295291;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 314159;\r\na_correct = 31416153708;\r\ny_correct = 3.141564629404888;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 3141592;\r\na_correct = 3141592912272;\r\ny_correct = 3.141591087728265;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 31415926;\r\na_correct = 314159277765514;\r\ny_correct = 3.141592422344870;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)   \r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-15T04:19:17.000Z","updated_at":"2026-03-16T11:10:09.000Z","published_at":"2021-03-15T04:33:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo commemorate Pi Day (March 14 in the U.S.), compute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term in a sequence by starting with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, rounding up to the next multiple of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n-1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, rounding up to the next multiple of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n-2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en-2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and so on to rounding up to the next multiple of 1. For example, with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 8, you would get 14, 18, 20, 20, 21, 22, and—the element in the sequence—\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 22. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term in this sequence. Also compute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n^2/f(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en^2/f(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and notice its limit as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e gets large. For more on this limit, see \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathpages.com/home/kmath001/kmath001.htm\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethis page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e by K.S. Brown.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56240,"title":"List numbers that are not squares","description":"The numbers 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, etc. are not perfect squares. Write a function to list the th term in this sequence. Check the test suite to see which functions are banned for this problem. For background music while solving this problem, you can listen to Dave Brubeck’s Unsquare Dance.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 340.408px 8px; transform-origin: 340.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe numbers 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, etc. are not perfect squares. Write a function to list the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.1083px 8px; transform-origin: 31.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term in this sequence. Check the test suite to see which functions are banned for this problem. For background music while solving this problem, you can listen to Dave Brubeck’s \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=lbdEzRfbeH4\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eUnsquare Dance\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = unsquare(n)\r\n  x = setdiff(1:n,(1:floor(sqrt(n))).^2);\r\n  y = x(n);\r\nend","test_suite":"%%\r\nn = 1:100;\r\ny_correct = [2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 46 47 48 50 51 52 53 54 55 56 57 58 59 60 61 62 63 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 101 102 103 104 105 106 107 108 109 110];\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 5075;\r\ny_correct = 5146;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 61086;\r\ny_correct = 61333;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 721097;\r\ny_correct = 721946;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8321008;\r\ny_correct = 8323893;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 94321019;\r\ny_correct = 94330731;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 123456789101112;\r\ny_correct = 123456800212223;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 9e15;\r\ny_correct = 9000000094868330;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nfiletext = fileread('unsquare.m');\r\nillegal = contains(filetext, '*') || contains(filetext, '^') || contains(filetext, 'conv') || contains(filetext, 'setdiff') || contains(filetext, 'prod') || ...\r\n          contains(filetext, '==') || contains(filetext, '~=') || contains(filetext, 'isequal') || contains(filetext, 'pow') || contains(filetext, 'nthroot') || ...\r\n          contains(filetext, 'times') || contains(filetext, 'eq') || contains(filetext, '/') || contains(filetext, 'div') || contains(filetext, 'det');\r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-10-07T03:22:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-07T03:17:26.000Z","updated_at":"2026-03-16T12:45:20.000Z","published_at":"2022-10-07T03:22:08.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe numbers 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, etc. are not perfect squares. Write a function to list the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term in this sequence. Check the test suite to see which functions are banned for this problem. For background music while solving this problem, you can listen to Dave Brubeck’s \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=lbdEzRfbeH4\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eUnsquare Dance\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47310,"title":"Find Logic 15","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 221.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 110.81px; transform-origin: 174px 110.81px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 64\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 25\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 8;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 25;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 216;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":449,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-05T14:25:25.000Z","updated_at":"2026-02-20T09:45:29.000Z","published_at":"2020-11-05T14:25:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 64\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":3010,"title":"Self-similarity 1 - Every other term","description":"Self-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003chttps://oeis.org/selfsimilar.html OEIS page\u003e for more information.\r\n\r\nIn this problem, you are to check if the sequence is self-similar by every other term. The problem set assumes that you use the easiest route: take the first element and then every other element thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\r\n\r\nFor example,\r\n\r\n* seq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]\r\n* seq_every_other = [0,  ,  1, , 1, , 2, , 1, , 2, , 2, , 3, ,] (extra commas are instructional and should not be in the every-other series) \r\n* seq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3]\r\n\r\nSince seq_every_other = seq_orig_first_half, the set is self-similar.\r\n\r\nThis problem is related to \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term Problem 3011\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms Problem 3012\u003e.","description_html":"\u003cp\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003ca href = \"https://oeis.org/selfsimilar.html\"\u003eOEIS page\u003c/a\u003e for more information.\u003c/p\u003e\u003cp\u003eIn this problem, you are to check if the sequence is self-similar by every other term. The problem set assumes that you use the easiest route: take the first element and then every other element thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\u003c/p\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cul\u003e\u003cli\u003eseq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]\u003c/li\u003e\u003cli\u003eseq_every_other = [0,  ,  1, , 1, , 2, , 1, , 2, , 2, , 3, ,] (extra commas are instructional and should not be in the every-other series)\u003c/li\u003e\u003cli\u003eseq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eSince seq_every_other = seq_orig_first_half, the set is self-similar.\u003c/p\u003e\u003cp\u003eThis problem is related to \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term\"\u003eProblem 3011\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms\"\u003eProblem 3012\u003c/a\u003e.\u003c/p\u003e","function_template":"function [tf] = self_similarity_1(seq)\r\n\r\ntf = 0;\r\n\r\nend","test_suite":"%%\r\nseq = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 0, 4, 8, 0, 0, 4, 4, 8, 0, 0, 8, 0, 0, 4, 8, 4, 0, 8, 0, 0, 0, 0, 12, 8, 0, 0, 8, 0, 0, 4, 0, 8, 0, 4, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 4, 12, 0, 8, 8, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, 4, 16, 0, 0, 8, 0, 0, 0, 4, 8, 8, 0, 0, 0, 0, 0, 8, 4, 8, 0, 0, 16, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 4, 0, 12, 8];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 2, 0, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 3, 3, 0, 0, 2, 1, 4, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 4, 0, 1, 2, 0, 3, 0, 4, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 3, 2, 3, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 2, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4, 9, 5, 6, 1, 7, 6, 11, 5, 14, 9, 13, 4, 15, 11, 18, 7, 17, 10, 13, 3, 14, 11, 19, 8, 21, 13, 18, 5, 17, 12, 19];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 6, 6, 30, 6, 30, 30, 54, 6, 102, 30, 78, 30, 78, 54, 150, 6, 102, 102, 126, 30, 270, 78, 150, 30, 150, 78, 318, 54, 174, 150, 198, 6, 390, 102, 270, 102, 222, 126, 390, 30, 246, 270, 270, 78, 510, 150, 294, 30, 390, 150, 510, 78, 318, 390, 390, 54, 630, 174, 366];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 2, 2, 1, 4, 2, 3, 2, 3, 2, 5, 1, 4, 4, 4, 2, 7, 3, 4, 2, 5, 3, 9, 2, 5, 5, 4, 1, 11, 4, 7, 4, 6, 4, 10, 2, 7, 7, 7, 3, 13, 4, 7, 2, 9, 5, 14, 3, 8, 9, 10, 2, 16, 8, 9, 5, 9, 5, 21, 1, 11, 11, 10, 4, 17, 7, 10, 4, 11, 6, 11, 4, 16, 10, 11, 2, 23, 7, 12, 7, 14, 7, 20, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 0, 2, 1, 1, 1, 0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 1, 2, 0, 0, 2, 1, 1, 2, 1, 1, 1, 1, 0, 2, 0, 0, 2, 2, 1, 2, 0, 1, 2, 0, 1, 3, 0, 0, 2, 1, 0, 2, 2, 1, 1, 0, 0, 3, 1, 2, 2, 1, 0, 2, 0, 1, 2, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 24, 24, 96, 24, 144, 96, 192, 24, 312, 144, 288, 96, 336, 192, 576, 24, 432, 312, 480, 144, 768, 288, 576, 96, 744, 336, 960, 192, 720, 576, 768, 24, 1152, 432, 1152, 312, 912, 480, 1344, 144, 1008, 768, 1056, 288, 1872, 576, 1152, 96, 1368, 744, 1728, 336];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 0, 2, 1, 1, 1, 0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 1, 2, 0, 0, 2, 1, 1, 2, 1, 1, 2, 1, 0, 2, 0, 0, 2, 2, 1, 2, 0, 1, 2, 0, 1, 3, 0, 0, 2, 1, 0, 2, 2, 1, 1, 0, 0, 3, 1, 2, 2, 1, 0, 2, 0, 1, 2, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 2, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 1, 2, 2, 0, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 3, 3, 0, 0, 2, 1, 4, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 4, 0, 1, 2, 0, 3, 0, 4, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 3, 2, 3, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 0, 4, 8, 0, 0, 4, 4, 8, 0, 0, 8, 0, 0, 4, 8, 4, 0, 8, 0, 0, 0, 0, 12, 8, 0, 0, 8, 0, 0, 4, 0, 8, 0, 4, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 4, 12, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 4, 16, 0, 0, 8, 0, 0, 0, 4, 8, 8, 0, 0, 0, 0, 0, 8, 4, 8, 0, 0, 16, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 4, 0, 12, 8];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, -1, 0, 1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -3, -2, 1, -1, 2, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, 1, -4, -3, 1, -2, 3, 1, -2, -1, 3, 2, -1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -1, 0, 1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -5, -4, 1, -3, 4, 1, -3, -2, 5, 3, -2, 1, -3, -2, 1, -1, 4, 3, -1, 2, -3, -1, 2, 1, -3, -2, 1, -1, 2, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3, 2, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 7, 6, 6, 5, 6, 5, 5, 4, 6, 5, 5, 4, 5, 4, 4, 3, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 24, 24, 96, 24, 144, 96, 192, 24, 312, 144, 288, 96, 336, 192, 576, 24, 432, 312, 480, 144, 768, 288, 576, 96, 744, 336, 960, 192, 720, 576, 768, 24, 1152, 432, 1152, 312, 912, 480, 1344, 312, 1008, 768, 1056, 288, 1872, 576, 1152, 96, 1368, 744, 1728, 336];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 4, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 16, 16, 8, 16, 16, 32, 8, 8, 16, 32, 16, 32, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 6, 6, 30, 6, 30, 30, 54, 6, 102, 30, 78, 30, 78, 54, 150, 6, 102, 102, 126, 30, 270, 78, 150, 30, 150, 78, 318, 54, 174, 150, 198, 6, 390, 102, 270, 102, 222, 126, 390, 30, 246, 270, 270, 78, 510, 150, 294, 30, 390, 150, 510, 78, 318, 318, 390, 54, 630, 174, 366];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 6, 5, 5, 4, 5, 3, 4, 3, 5, 4, 4, 3, 4, 3, 3, 2, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 7, 6, 6, 5, 6, 5, 5, 4, 6, 5, 5, 4, 5, 4, 4, 3, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 2, 2, 1, 4, 2, 3, 2, 3, 2, 5, 1, 4, 4, 4, 2, 7, 3, 4, 2, 5, 3, 9, 2, 5, 5, 5, 1, 11, 4, 7, 4, 6, 4, 10, 2, 7, 7, 7, 3, 13, 4, 7, 2, 9, 5, 14, 3, 8, 9, 10, 2, 16, 5, 9, 5, 9, 5, 21, 1, 11, 11, 10, 4, 17, 7, 10, 4, 11, 6, 18, 4, 16, 10, 11, 2, 23, 7, 12, 7, 14, 7, 20, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, -1, 0, 1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -3, -2, 1, -1, 2, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, -1, -4, -3, 1, -2, 3, 1, -2, -1, 3, 2, -1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -1, 0, 1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -5, -4, 1, -3, 4, 1, -3, -2, 5, 3, -2, 1, -3, -2, 1, -1, 4, 3, -1, 2, -3, -1, 2, 1, -3, -2, 1, -1, 2, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4, 9, 5, 6, 1, 7, 6, 11, 5, 14, 9, 13, 4, 15, 11, 18, 7, 17, 10, 13, 3, 14, 11, 19, 8, 21, 13, 18, 5, 17, 12, 19];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":72,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":30,"created_at":"2015-02-13T04:04:32.000Z","updated_at":"2026-03-16T14:11:36.000Z","published_at":"2015-02-13T04:04:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/selfsimilar.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOEIS page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more information.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, you are to check if the sequence is self-similar by every other term. The problem set assumes that you use the easiest route: take the first element and then every other element thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_every_other = [0, , 1, , 1, , 2, , 1, , 2, , 2, , 3, ,] (extra commas are instructional and should not be in the every-other series)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince seq_every_other = seq_orig_first_half, the set is self-similar.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is related to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3011\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3012\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45384,"title":"Sum! Sum! Sum!","description":"Calculate the sum of the sequence up to nth term \u003e\u003e \r\n\r\n  a,aa,aaa,aaaa,... \r\n  2,22,222,2222,...  [for a=2]","description_html":"\u003cp\u003eCalculate the sum of the sequence up to nth term \u0026gt;\u0026gt;\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ea,aa,aaa,aaaa,... \r\n2,22,222,2222,...  [for a=2]\r\n\u003c/pre\u003e","function_template":"function  y = series_sum(a,n)","test_suite":"%%\r\nassert(isequal(series_sum(3,4),3702))\r\n%%\r\nassert(isequal(series_sum(2,15),246913580246910))\r\n%%\r\nassert(isequal(series_sum(9,9),1111111101))\r\n%%\r\nassert(isequal(series_sum(1,12),123456790122))\r\n%%\r\nassert(isequal(series_sum(5,5),61725))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-03-24T13:05:35.000Z","updated_at":"2026-03-05T07:10:14.000Z","published_at":"2020-03-24T13:05:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the sum of the sequence up to nth term \u0026gt;\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[a,aa,aaa,aaaa,... \\n2,22,222,2222,...  [for a=2]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44544,"title":"Normie Function (2)","description":"Another _Normie Function_ defined as _f(n)= f(n-1)+f(n-2)+f(n-3)_ , *when n\u003e3* and _1_ , *when n\u003c=3*. *Find the nth term of this function* .","description_html":"\u003cp\u003eAnother \u003ci\u003eNormie Function\u003c/i\u003e defined as \u003ci\u003ef(n)= f(n-1)+f(n-2)+f(n-3)\u003c/i\u003e , \u003cb\u003ewhen n\u0026gt;3\u003c/b\u003e and \u003ci\u003e1\u003c/i\u003e , \u003cb\u003ewhen n\u0026lt;=3\u003c/b\u003e. \u003cb\u003eFind the nth term of this function\u003c/b\u003e .\u003c/p\u003e","function_template":"function y = normie(n)\r\n  y = n;\r\nend","test_suite":"%%\r\nn = 3;\r\ny_correct = 1;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 23;\r\ny_correct = 289329;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 36;\r\ny_correct = 797691075;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 37;\r\ny_correct = 1467182629;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 40;\r\ny_correct = 9129195487;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 50;\r\ny_correct = 4045078385041;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 70;\r\ny_correct = 794174268033812736;\r\nassert(isequal(normie(n),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":104442,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2018-03-28T11:02:45.000Z","rescore_all_solutions":false,"group_id":61,"created_at":"2018-03-22T09:27:39.000Z","updated_at":"2026-03-16T11:16:28.000Z","published_at":"2018-03-22T09:27:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnother\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNormie Function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e defined as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef(n)= f(n-1)+f(n-2)+f(n-3)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhen n\u0026gt;3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhen n\u0026lt;=3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFind the nth term of this function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45253,"title":"Pell numbers ","description":"Find the nth pell number\r\n\r\n\r\n\u003chttps://en.wikipedia.org/wiki/Pell_number\u003e","description_html":"\u003cp\u003eFind the nth pell number\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Pell_number\"\u003ehttps://en.wikipedia.org/wiki/Pell_number\u003c/a\u003e\u003c/p\u003e","function_template":"function p=pell_seq(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nn = 3;\r\ny_correct = 2;\r\nassert(isequal(pell_seq(n),y_correct))\r\n%%\r\nn = 6;\r\ny_correct = 29;\r\nassert(isequal(pell_seq(n),y_correct))\r\n%%\r\nn = 9;\r\ny_correct = 408;\r\nassert(isequal(pell_seq(n),y_correct))\r\n%%\r\nn = 12;\r\ny_correct = 5741;\r\nassert(isequal(pell_seq(n),y_correct))\r\n%%\r\nn = 15;\r\ny_correct = 80782;\r\nassert(isequal(pell_seq(n),y_correct))\r\n\r\n%%\r\nn = 19;\r\ny_correct = 2744210;\r\nassert(isequal(pell_seq(n),y_correct))\r\n\r\n%%\r\nn = 23;\r\ny_correct = 93222358;\r\nassert(isequal(pell_seq(n),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":77,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-03T18:34:11.000Z","updated_at":"2026-01-16T23:48:17.000Z","published_at":"2020-01-03T18:35:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the nth pell number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Pell_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Pell_number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":51002,"title":"Deduce the pattern behind the sequence","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 917.917px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 458.958px; transform-origin: 407px 458.958px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60.075px 7.91667px; transform-origin: 60.075px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHere's a sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.075px 7.91667px; transform-origin: 37.075px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTricky? Not!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46.6px 7.91667px; transform-origin: 46.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou'll deduce it\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 7.91667px; transform-origin: 44.3333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFrom this plot.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49px 7.91667px; transform-origin: 49px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the plot gives \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.0917px 7.91667px; transform-origin: 44.0917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou the blues,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.5667px 7.91667px; transform-origin: 64.5667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe test suite should\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0167px 7.91667px; transform-origin: 63.0167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eProvide some clues.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.9167px 7.91667px; transform-origin: 52.9167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFeeling anxious?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.15px 7.91667px; transform-origin: 41.15px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou'll be fine.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.1167px 7.91667px; transform-origin: 52.1167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe code I wrote\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.3417px 7.91667px; transform-origin: 51.3417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIs one short line.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 497.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 248.958px; text-align: left; transform-origin: 384px 248.958px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 657px;height: 492px\" 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\" data-image-state=\"image-loaded\" width=\"657\" height=\"492\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = mysterySeq(n)\r\n  a = f(n);\r\nend","test_suite":"%%\r\nassert(isequal(mysterySeq(2),2))\r\n\r\n%%\r\nassert(isequal(mysterySeq(4),4))\r\n\r\n%%\r\nassert(isequal(mysterySeq(9),6))\r\n\r\n%%\r\nassert(isequal(mysterySeq(15),8))\r\n\r\n%%\r\nassert(isequal(mysterySeq(36),10))\r\n\r\n%%\r\nassert(isequal(mysterySeq(35),12))\r\n\r\n%%\r\nassert(isequal(mysterySeq(144),14))\r\n\r\n%%\r\nassert(isequal(mysterySeq(256),16))\r\n\r\n%%\r\nassert(isequal(mysterySeq(315),18))\r\n\r\n%%\r\nassert(isequal(mysterySeq(441),20))\r\n\r\n%%\r\nassert(isequal(mysterySeq(495),22))\r\n\r\n%%\r\nassert(isequal(mysterySeq(143),24))\r\n\r\n%%\r\nassert(isequal(mysterySeq(169),26))\r\n\r\n%%\r\nassert(isequal(mysterySeq(115),28))\r\n\r\n%%\r\nassert(isequal(mysterySeq(4802),30))\r\n\r\n%%\r\nassert(isequal(mysterySeq(65536),32))\r\n\r\n%%\r\nassert(isequal(mysterySeq(62500),34))\r\n\r\n%%\r\nassert(isequal(mysterySeq(186),36))\r\n\r\n%%\r\nassert(isequal(mysterySeq(361),38))\r\n\r\n%%\r\nassert(isequal(mysterySeq(1048576),40))\r\n\r\n%%\r\nassert(isequal(mysterySeq(117649),42))\r\n\r\n%%\r\nassert(isequal(mysterySeq(14641),44))\r\n\r\n%%\r\nassert(isequal(mysterySeq(529),46))\r\n\r\n%%\r\nassert(isequal(mysterySeq(116875),48))\r\n\r\n%%\r\nassert(isequal(mysterySeq(301),50))\r\n\r\n%%\r\nassert(isequal(mysterySeq(235),52))\r\n\r\n%%\r\nassert(isequal(mysterySeq(329),54))\r\n\r\n%%\r\nassert(isequal(mysterySeq(159),56))\r\n\r\n%%\r\nassert(isequal(mysterySeq(517),58))\r\n\r\n%%\r\nassert(isequal(mysterySeq(3486784401),60))\r\n\r\n%%\r\nassert(isequal(mysterySeq(444125),62))\r\n\r\n%%\r\nassert(isequal(mysterySeq(96049800),64))\r\n\r\n%%\r\nassert(isequal(mysterySeq(31381059609),66))\r\n\r\n%%\r\nassert(isequal(mysterySeq(533715),68))\r\n\r\n%%\r\nassert(isequal(mysterySeq(282475249),70))\r\n\r\n%%\r\nassert(isequal(mysterySeq(36501),72))\r\n\r\n%%\r\nassert(isequal(mysterySeq(1369),74))\r\n\r\n%%\r\nassert(isequal(mysterySeq(130321),76))\r\n\r\n%%\r\nassert(isequal(mysterySeq(46023),78))\r\n\r\n%%\r\nassert(isequal(mysterySeq(576650390625),80))\r\n\r\n%%\r\nassert(isequal(mysterySeq(1172889),82))\r\n\r\n%%\r\nassert(isequal(mysterySeq(13841287201),84))\r\n\r\n%%\r\nassert(isequal(mysterySeq(22755),86))\r\n\r\n%%\r\nassert(isequal(mysterySeq(2133),88))\r\n\r\n%%\r\nassert(isequal(mysterySeq(8033333),90))\r\n\r\n%%\r\nassert(isequal(mysterySeq(267),92))\r\n\r\n%%\r\nassert(isequal(mysterySeq(102656268),94))\r\n\r\n%%\r\nassert(isequal(mysterySeq(16168),96))\r\n\r\n%%\r\nassert(isequal(mysterySeq(228125),98))\r\n\r\n%%\r\nassert(isequal(mysterySeq(1125899906842624),100))\r\n\r\n%%\r\np = primes(1e4); k = randi(length(p));\r\nassert(isequal(mysterySeq(p(k)),p(k)))\r\n\r\n%%\r\nassert(isequal(mysterySeq(mysterySeq(mysterySeq(mysterySeq(mysterySeq(mysterySeq(50014)))))),5))","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2021-03-18T00:35:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-17T02:24:34.000Z","updated_at":"2025-12-15T15:32:30.000Z","published_at":"2021-03-17T02:29:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere's a sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTricky? Not!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou'll deduce it\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFrom this plot.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the plot gives \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou the blues,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test suite should\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProvide some clues.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFeeling anxious?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou'll be fine.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe code I wrote\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIs one short line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"492\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"657\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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unique orderings of vertices of a polygon","description":"Cody Problem 2671 asks us to determine whether four points can be the corners of a rectangle. The points are not necessarily input in order (either clockwise or counterclockwise). My initial attempt at the problem involved determining how the points might be presented. If the corners are numbered as shown below, then they can be input in 24 ways.\r\nHowever, for the rectangle problem, many of the 24 ways are essentially the same. For example, 2341, 3214, and 4123 are effectively the same as 1234 because the numbers of the corners could be shifted around the rectangle. In fact, only three of the 24 ways are different (1234, 1243, and 1324). \r\nWrite a function to determine the unique orderings of vertices of a polygon with  sides. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 356.917px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 178.458px; transform-origin: 407px 178.458px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/2671\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 2671\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 294.433px 7.91667px; transform-origin: 294.433px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asks us to determine whether four points can be the corners of a rectangle. The points are not necessarily input in order (either clockwise or counterclockwise). My initial attempt at the problem involved determining how the points might be presented. If the corners are numbered as shown below, then they can be input in 24 ways.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.133px 7.91667px; transform-origin: 383.133px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHowever, for the rectangle problem, many of the 24 ways are essentially the same. For example, 2341, 3214, and 4123 are effectively the same as 1234 because the numbers of the corners could be shifted around the rectangle. In fact, only three of the 24 ways are different (1234, 1243, and 1324). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 245.317px 7.91667px; transform-origin: 245.317px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine the unique orderings of vertices of a polygon with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.1667px 7.91667px; transform-origin: 22.1667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sides. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 182.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 91.4583px; text-align: left; transform-origin: 384px 91.4583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 262px;height: 177px\" 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data-image-state=\"image-loaded\" width=\"262\" height=\"177\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = polyVert(n)\r\n  y = nchoosek(2*n,n);\r\nend","test_suite":"%% Rectangle\r\nassert(isequal(polyVert(4),3))\r\n\r\n%% Triangle\r\nassert(isequal(polyVert(3),1))\r\n\r\n%% Heptagon\r\nassert(isequal(polyVert(7),360))\r\n\r\n%% Dodecagon\r\nassert(isequal(polyVert(12),19958400))\r\n\r\n%% Heptadecagon\r\nassert(isequal(polyVert(17),10461394944000))\r\n\r\n%% \r\nd = num2str(polyVert(19))-'0';\r\np = polyval(d(1:3:end),4);\r\np_correct = 3760;\r\nassert(isequal(p,p_correct))\r\n\r\n%% \r\nd = num2str(polyVert(15));\r\ns = polyVert(str2num(d(4)))+polyVert(str2num(d(6:7)));\r\ns_correct = 3113512920;\r\nassert(isequal(s,s_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-27T04:52:02.000Z","updated_at":"2026-01-15T18:13:53.000Z","published_at":"2021-05-27T04:56:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/2671\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 2671\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks us to determine whether four points can be the corners of a rectangle. The points are not necessarily input in order (either clockwise or counterclockwise). My initial attempt at the problem involved determining how the points might be presented. If the corners are numbered as shown below, then they can be input in 24 ways.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHowever, for the rectangle problem, many of the 24 ways are essentially the same. For example, 2341, 3214, and 4123 are effectively the same as 1234 because the numbers of the corners could be shifted around the rectangle. In fact, only three of the 24 ways are different (1234, 1243, and 1324). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine the unique orderings of vertices of a polygon with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e sides. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml 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sequence revisited","description":"This problem is related to \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42835-return-the-sequence-element-ii Problem 42835\u003e.\r\n\r\nFor any starting positive integer, a(1) = x, the \u003chttps://en.wikipedia.org/wiki/Juggler_sequence Juggler sequence\u003e is defined by:\r\n\r\na(i+1) = floor(a(i)^0.5) , for even a(i).\r\n\r\na(i+1) = floor(a(i)^1.5) , for odd a(i).\r\n\r\nWhen a Juggler sequence reaches 1, all subsequent elements will also be 1s.\r\n\r\nLet l(x) be the number of Juggler sequence iterations required to reach 1 with a starting value of x.\r\n\r\nLet h(x) be the maximum value of a Juggler sequence with a starting value of x.\r\n\r\nGiven x, return l(x) and h(x).\r\n\r\nExample:\r\n\r\nx = 3\r\n\r\nl = 6\r\n\r\nh = 36","description_html":"\u003cp\u003eThis problem is related to \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42835-return-the-sequence-element-ii\"\u003eProblem 42835\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eFor any starting positive integer, a(1) = x, the \u003ca href = \"https://en.wikipedia.org/wiki/Juggler_sequence\"\u003eJuggler sequence\u003c/a\u003e is defined by:\u003c/p\u003e\u003cp\u003ea(i+1) = floor(a(i)^0.5) , for even a(i).\u003c/p\u003e\u003cp\u003ea(i+1) = floor(a(i)^1.5) , for odd a(i).\u003c/p\u003e\u003cp\u003eWhen a Juggler sequence reaches 1, all subsequent elements will also be 1s.\u003c/p\u003e\u003cp\u003eLet l(x) be the number of Juggler sequence iterations required to reach 1 with a starting value of x.\u003c/p\u003e\u003cp\u003eLet h(x) be the maximum value of a Juggler sequence with a starting value of x.\u003c/p\u003e\u003cp\u003eGiven x, return l(x) and h(x).\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003ex = 3\u003c/p\u003e\u003cp\u003el = 6\u003c/p\u003e\u003cp\u003eh = 36\u003c/p\u003e","function_template":"function [l h] = juggler(x)\r\n  l = x;\r\n  h = x;\r\nend","test_suite":"%%\r\nx = 3;\r\nl_correct = 6;\r\nh_correct = 36;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 5;\r\nl_correct = 5;\r\nh_correct = 36;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 10;\r\nl_correct = 7;\r\nh_correct = 36;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 77;\r\nl_correct = 19;\r\nh_correct = 2322378;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 99;\r\nl_correct = 11;\r\nh_correct = 37754276;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 117;\r\nl_correct = 11;\r\nh_correct = 44992;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 1;\r\nl_correct = 0;\r\nh_correct = 1;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 2;\r\nl_correct = 1;\r\nh_correct = 2;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-27T19:30:07.000Z","updated_at":"2025-12-31T12:07:49.000Z","published_at":"2016-04-27T19:30:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is related to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42835-return-the-sequence-element-ii\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 42835\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor any starting positive integer, a(1) = x, the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Juggler_sequence\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eJuggler sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is defined by:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(i+1) = floor(a(i)^0.5) , for even a(i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(i+1) = floor(a(i)^1.5) , for odd a(i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen a Juggler sequence reaches 1, all subsequent elements will also be 1s.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet l(x) be the number of Juggler sequence iterations required to reach 1 with a starting value of x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet h(x) be the maximum value of a Juggler sequence with a starting value of x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven x, return l(x) and h(x).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003el = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eh = 36\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61052,"title":"Compute the Dedekind psi function","description":"Write a function to compute the Dedekind psi function. The values for n = 1, 2, 3, 4, 5, and 6 are 1, 3, 4, 6, 6, and 12. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 10.5px; transform-origin: 408px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/DedekindFunction.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eDedekind psi function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The values for n = 1, 2, 3, 4, 5, and 6 are 1, 3, 4, 6, 6, and 12. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = DedekindPsi(n)\r\n  y = psi(n);\r\nend","test_suite":"%%\r\nn = 1;\r\ny = DedekindPsi(n);\r\ny_correct = 1;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8;\r\ny = DedekindPsi(n);\r\ny_correct = 12;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 49;\r\ny = DedekindPsi(n);\r\ny_correct = 56;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 312;\r\ny = DedekindPsi(n);\r\ny_correct = 672;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1441;\r\ny = DedekindPsi(n);\r\ny_correct = 1584;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8028;\r\ny = DedekindPsi(n);\r\ny_correct = 16128;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 14035;\r\ny = DedekindPsi(n);\r\ny_correct = 19296;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 85432;\r\ny = DedekindPsi(n);\r\ny_correct = 131040;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 6645344;\r\ny = DedekindPsi(n);\r\ny_correct = 10402560;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 5533221188;\r\ny = DedekindPsi(n);\r\ny_correct = 9083498112;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\np = primes(1e8);\r\nq = p(randi(length(p)));\r\ny = DedekindPsi(q);\r\nassert(isequal(y,q+1))\r\n\r\n%%\r\np = primes(200);\r\nq = p(randi(length(p)));\r\nn = randi(5);\r\nx = q^n;\r\ny = DedekindPsi(x);\r\nassert(isequal(y,x+x/q))\r\n\r\n%%\r\np = primes(200);\r\nk = unique(randi(length(p),[1 randi(5)]));\r\nq = p(k);\r\nx = prod(q);\r\ny = DedekindPsi(x);\r\nassert(isequal(y,prod(q+1)))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2025-10-25T15:14:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-10-25T15:09:34.000Z","updated_at":"2026-02-26T13:49:01.000Z","published_at":"2025-10-25T15:14:46.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/DedekindFunction.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDedekind psi function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The values for n = 1, 2, 3, 4, 5, and 6 are 1, 3, 4, 6, 6, and 12. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47295,"title":"Find Logic 13","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 221.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 110.81px; transform-origin: 174px 110.81px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 100\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 102\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 99\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 103\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 98\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of logic\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 100;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 100;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\nassert(isequal(logic(x),102))\r\n\r\n%%\r\nx = 4;\r\nassert(isequal(logic(x),103))\r\n\r\n%%\r\nx = 7;\r\nassert(isequal(logic(x),97))","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":403,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-05T07:07:30.000Z","updated_at":"2026-02-14T07:02:11.000Z","published_at":"2020-11-05T07:07:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 102\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 99\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 103\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 98\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of logic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51274,"title":"Solve a nonlinear difference equation","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 95.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 47.875px; transform-origin: 407px 47.875px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 44.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.25px; text-align: left; transform-origin: 384px 22.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.967px 7.91667px; transform-origin: 102.967px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider the difference equation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-8px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a_{n+1} = a_n^p\" style=\"width: 60.5px; height: 22px;\" width=\"60.5\" height=\"22\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.2333px 7.91667px; transform-origin: 48.2333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the initial (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n = 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.95px 7.91667px; transform-origin: 22.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.70833px 7.91667px; transform-origin: 9.70833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 7.91667px; transform-origin: 28.3917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 2 and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = 2\" style=\"width: 38px; height: 18px;\" width=\"38\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 7.91667px; transform-origin: 19.4417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a1 = 4\" style=\"width: 41.5px; height: 20px;\" width=\"41.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a2 = 16\" style=\"width: 49px; height: 20px;\" width=\"49\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a3 = 256\" style=\"width: 56.5px; height: 20px;\" width=\"56.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.1px 7.91667px; transform-origin: 17.1px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, etc. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.125px; text-align: left; transform-origin: 384px 21.125px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.492px 7.91667px; transform-origin: 125.492px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes two values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.475px 7.91667px; transform-origin: 103.475px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the corresponding values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABNklEQVRYhe2VUbWDMAyGPw84wAAGqgAFOKgDHMwCGpBQD1hAAxbYA8lpxsrY4ZTdh9vvnD4sWfPTpEmhUCgUCoU/ogE80ANObE5+N3eKBmAWcQcMwASssuo7hDsJPgPVzrca30+Frfgjt3BrgruEvz7xX6YCFgk8HvxHs7KQzspleuKpjm5xEH/IKQzx1EeBnfm4PqfwN4ED55m5hE15m/B7YmZurfdevGNru5HXsgzELPXin9hasBL/KraPNEY8yOZKgmq/68kHWfuO0LK04nfEaXg6CfVkdo3EFC87+55FPjQQZ8As66sx3LKd1ic2fHpMbOa82HQgHc2MbOidmYiZ0oHkjzblQuvdGZteuNueXSX1EM3GlmrfLOiAsrXVOzCwtd5t4g/e50PNdvsXXktRKBT+CU+MO3Oqf1KjkgAAAABJRU5ErkJggg==\" alt=\"a_n\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.5833px 7.91667px; transform-origin: 85.5833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand returns the initial value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.225px 7.91667px; transform-origin: 27.225px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the exponent \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p,a0] = recurrence1(n,a)\r\n  p = f1(n,a);\r\n  a0 = f2(n,a);\r\nend","test_suite":"%%\r\na = [16 65536];\r\nn = [2 4];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 2;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [512 134217728];\r\nn = [2 3];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 3;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [4.756828460010884 2684.848561202718];\r\nn = [2 6];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 3/2;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [4.756828460010884 2684.848561202718];\r\nn = [2 6];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 3/2;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [0.840896415253715 0.999994711720674];\r\nn = [2 17];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 1/2;\r\na0_correct = 1/2;\r\nassert(abs(p-p_correct)\u003c1e-10 \u0026\u0026 abs(a0-a0_correct)\u003c1e-10)\r\n\r\n%%\r\na = [3.236570233533632 6.5197372744901154];\r\nn = [53 100];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 1.01;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [27.065907669081142 6576132142.795870];\r\nn = [4 8];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = (1+sqrt(5))/2;\r\na0_correct = (1+sqrt(5))/2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [1.033024879021228 1.000000123944382];\r\nn = [2 8];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 1/8;\r\na0_correct = 8;\r\nassert(abs(p-p_correct)\u003c1e-10 \u0026\u0026 abs(a0-a0_correct)\u003c1e-9)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-04-02T16:23:14.000Z","updated_at":"2026-01-13T13:35:21.000Z","published_at":"2021-04-02T16:27:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the difference equation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a_{n+1} = a_n^p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_{n+1} = a_n^p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with the initial (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 2 and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = 2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a1 = 4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_1 = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a2 = 16\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_2 = 16\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a3 = 256\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_3= 256\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, etc. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes two values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the corresponding values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a_n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand returns the initial value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the exponent \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47370,"title":"Find Logic 25","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 191.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 95.8333px; transform-origin: 174px 95.8333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(11) = 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(15) = 6\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(22) = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return value according to logic in problem\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 11;\r\ny_correct = 2;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 15;\r\ny_correct = 6;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":234,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-06T13:48:01.000Z","updated_at":"2026-02-14T13:45:20.000Z","published_at":"2020-11-06T13:48:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(11) = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(15) = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(22) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return value according to logic in problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47345,"title":"Find Logic 20","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 251.571px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 125.786px; transform-origin: 174px 125.786px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 7\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(6) = 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 7;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 7;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 4;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\nassert(isequal(logic(x),9))\r\n\r\n%%\r\nx = 6;\r\nassert(isequal(logic(x),2))","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":365,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-06T05:30:27.000Z","updated_at":"2026-03-17T20:15:27.000Z","published_at":"2020-11-06T05:30:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(6) = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56593,"title":"List the nth term of Rozhenko’s inventory sequence","description":"Consider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\r\n0\r\n1, 1, 0\r\n2, 2, 2, 0\r\n3, 2, 4, 1, 1, 0\r\n4, 4, 4, 1, 4, 0\r\nWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19th term is 4. \r\nThis sequence produces interesting plots and music. See the related Numberphile video for more. \r\nWrite a function to report the th term of this sequence. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 345px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 172.5px; transform-origin: 407px 172.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.6px 8px; transform-origin: 374.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1, 1, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.2167px 8px; transform-origin: 27.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2, 2, 2, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7667px 8px; transform-origin: 42.7667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3, 2, 4, 1, 1, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7667px 8px; transform-origin: 42.7667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4, 4, 4, 1, 4, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e term is 4. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.425px 8px; transform-origin: 112.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis sequence produces interesting \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A342585/graph\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eplots\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/play?seq=A342585\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003emusic\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.275px 8px; transform-origin: 18.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. See \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=rBU9E-ZOZAI\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ethe related Numberphile video\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.8833px 8px; transform-origin: 31.8833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for more. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.1px 8px; transform-origin: 90.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to report the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.5583px 8px; transform-origin: 78.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term of this sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Rozhenko(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 19;\r\ny_correct = 4;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 53;\r\ny_correct = 5;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 347;\r\ny_correct = 25;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 823;\r\ny_correct = 27;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 1997;\r\ny_correct = 20;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 4721;\r\ny_correct = 68;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 13859;\r\ny_correct = 18;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 19793;\r\ny_correct = 7;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 24677;\r\ny_correct = 51;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 41903;\r\ny_correct = 357;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 25537;\r\ny_correct = 4;\r\nassert(isequal(Rozhenko(Rozhenko(Rozhenko(n))),y_correct))\r\n\r\n%%\r\nn = [1 4 8 14 20 28 37 46 57 69 82 95 110 125 142 159 177 196 216 238 260 285 310 335 362 390 418 448 478 511];\r\na = arrayfun(@Rozhenko,n);\r\ns_correct = 0;\r\nassert(isequal(sum(a),s_correct))\r\n\r\n%%\r\nfiletext = fileread('Rozhenko.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-11-13T14:07:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-11-13T04:07:55.000Z","updated_at":"2026-01-24T12:19:36.000Z","published_at":"2022-11-13T04:08:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1, 1, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2, 2, 2, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3, 2, 4, 1, 1, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4, 4, 4, 1, 4, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e term is 4. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis sequence produces interesting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A342585/graph\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eplots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/play?seq=A342585\\\"\u003e\u003cw:r\u003e\u003cw:t\u003emusic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. See \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=rBU9E-ZOZAI\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ethe related Numberphile video\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to report the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term of this sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60266,"title":"Stern-Brocot Sequence","description":"The Stern-Brocot diatomic sequence is defined as follows:\r\n\r\nThe first elements of the sequence are 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3.\r\nWrite a function to compute  for a given .\r\nSee https://oeis.org/A002487","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 214.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343.5px 107.25px; transform-origin: 343.5px 107.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.5px; text-align: left; transform-origin: 320.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Stern-Brocot diatomic sequence is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 93px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 46.5px; text-align: left; transform-origin: 320.5px 46.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-41px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"115\" height=\"93\" style=\"width: 115px; height: 93px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.5px; text-align: left; transform-origin: 320.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first elements of the sequence are 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 11.25px; text-align: left; transform-origin: 320.5px 11.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14\" height=\"20\" style=\"width: 14px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for a given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.5px; text-align: left; transform-origin: 320.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSee \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A002487\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://oeis.org/A002487\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = stern_brocot(n)\r\n\r\nend","test_suite":"all_glo = [0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4, 9, 5, 6, 1, 7, 6, 11, 5, 14, 9, 13, 4, 15, 11, 18, 7, 17, 10, 13, 3, 14, 11, 19, 8, 21, 13, 18, 5, 17, 12, 19, 7, 16, 9, 11, 2, 11, 9, 16, 7, 19, 12, 17, 5, 18, 13, 21, 8, 19, 11, 14, 3, 13, 10, 17, 7, 18, 11, 15, 4, 13, 9, 14, 5, 11, 6, 7, 1, 8, 7, 13, 6, 17, 11, 16, 5, 19, 14, 23, 9, 22, 13, 17, 4, 19, 15, 26, 11, 29, 18, 25, 7, 24, 17, 27, 10, 23, 13, 16, 3, 17, 14, 25, 11, 30, 19, 27, 8, 29, 21, 34, 13, 31, 18, 23, 5, 22, 17, 29, 12, 31, 19, 26, 7, 23, 16, 25, 9, 20, 11, 13, 2, 13, 11, 20, 9, 25, 16, 23, 7, 26, 19, 31, 12, 29, 17, 22, 5, 23, 18, 31, 13, 34, 21, 29, 8, 27, 19, 30, 11, 25, 14, 17, 3, 16, 13, 23, 10, 27, 17, 24, 7, 25, 18, 29, 11, 26, 15, 19, 4, 17, 13, 22, 9, 23, 14, 19, 5, 16, 11, 17, 6, 13, 7, 8, 1, 9, 8, 15, 7, 20, 13, 19, 6, 23, 17, 28, 11, 27, 16];\r\nn = randi([101,numel(all_glo)]) \r\ny_correct = all_glo(n+1)\r\n\r\n%%\r\n% n and y_correct are displayed but their definition is hidden.\r\nn\r\ny_obtained = stern_brocot(n)\r\ny_correct\r\nassert(isequal(y_obtained,y_correct));\r\n\r\n\r\n%%\r\nn = 100\r\ny_obtained = stern_brocot(n)\r\ny_correct = 7\r\nassert(isequal(y_obtained,y_correct));\r\n\r\n%%\r\nyy_correct = [0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3];\r\nfor n = 0:numel(yy_correct)-1\r\n    y_obtained = stern_brocot(n);\r\n    y_correct = yy_correct(n+1);\r\n    assert(isequal(y_obtained,y_correct));\r\nend\r\n\r\n%% \r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-11T16:21:06.000Z","updated_at":"2026-03-24T12:11:40.000Z","published_at":"2024-05-11T16:21:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Stern-Brocot diatomic sequence is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$$\\\\begin{cases} s_0=0,\\\\\\\\   s_1=1,\\\\\\\\ s_{2n} = s_n,\\\\\\\\ s_{2n+1} = s_n+s_{n+1} \\\\end{cases}$$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first elements of the sequence are 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for a given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A002487\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://oeis.org/A002487\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50913,"title":"Compute the nth term from the golden sieve","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.5px; transform-origin: 407px 82.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45367\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 45367\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129.5px 8px; transform-origin: 129.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved the Sieve of Eratosthenes, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/50811-compute-the-nth-term-from-the-sieve-of-flavius-josephus\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 50811\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94px 8px; transform-origin: 94px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved the Sieve of Flavius Josephus. To apply the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003egolden sieve\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133.5px 8px; transform-origin: 133.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, start with the natural numbers and at the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129px 8px; transform-origin: 129px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth step, take the sequence, which we will call \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87px 8px; transform-origin: 87px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and delete the term in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a(n)\" style=\"width: 29.5px; height: 18.5px;\" width=\"29.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.5px 8px; transform-origin: 30.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e position. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 119.5px 8px; transform-origin: 119.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the first step, delete the term in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 56px; height: 18.5px;\" width=\"56\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 231.5px 8px; transform-origin: 231.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e position to get 2, 3, 4, 5, 6, 7,…Then in the second step, delete the term in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a(2) = 3\" style=\"width: 56px; height: 18.5px;\" width=\"56\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 256px 8px; transform-origin: 256px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e position (i.e., 4) to get 2, 3, 5, 6, 7, 8, 9,…In the third step, delete the term in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a(3) = 5\" style=\"width: 56px; height: 18.5px;\" width=\"56\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.7167px 8px; transform-origin: 52.7167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e position (i.e., 7) to get 2, 3, 5, 6, 8, 9, 10,…Et cetera.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102px 8px; transform-origin: 102px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 178.5px 8px; transform-origin: 178.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term in the sequence after an infinite number of steps.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = goldenSieve(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 6; \r\ny_correct = 10;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 16; \r\ny_correct = 26;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 60; \r\ny_correct = 97;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 616; \r\ny_correct = 997;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1666; \r\ny_correct = 2696;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 6066; \r\ny_correct = 9815;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 16166; \r\ny_correct = 26157;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 66616; \r\ny_correct = 107787;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 166666; \r\ny_correct = 269671;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 606606; \r\ny_correct = 981509;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 161161616; \r\ny_correct = 260764972;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 6161161616; \r\ny_correct = 9968968905;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 616161161616; \r\ny_correct = 996969702042;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-12T02:43:21.000Z","updated_at":"2025-12-17T13:39:40.000Z","published_at":"2021-03-12T02:52:22.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45367\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 45367\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved the Sieve of Eratosthenes, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/50811-compute-the-nth-term-from-the-sieve-of-flavius-josephus\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 50811\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved the Sieve of Flavius Josephus. To apply the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egolden sieve\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, start with the natural numbers and at the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth step, take the sequence, which we will call \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and delete the term in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e position. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the first step, delete the term in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e position to get 2, 3, 4, 5, 6, 7,…Then in the second step, delete the term in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a(2) = 3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(2) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e position (i.e., 4) to get 2, 3, 5, 6, 7, 8, 9,…In the third step, delete the term in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a(3) = 5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(3) = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e position (i.e., 7) to get 2, 3, 5, 6, 8, 9, 10,…Et cetera.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term in the sequence after an infinite number of steps.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":48025,"title":"Find the Pattern 2","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 141px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 70.5px; transform-origin: 407px 70.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the pattern for the following sequence:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(1) = 98\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(2) = 92\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(5) = 50\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCreate a function which satisfies the pattern shown above.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pat(x)\r\n  y = x+2*x+3*x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 98;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 5;\r\ny_correct = 50;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 11;\r\ny_correct = -142;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 3;\r\ny_correct = 82;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 3.5;\r\ny_correct = 75.5;\r\nassert(isequal(pat(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":237,"test_suite_updated_at":"2020-12-17T19:02:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-17T18:57:25.000Z","updated_at":"2026-03-20T14:58:53.000Z","published_at":"2020-12-17T19:02:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the pattern for the following sequence:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(1) = 98\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(2) = 92\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(5) = 50\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a function which satisfies the pattern shown above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52283,"title":"Find numbers in the Popular Computing Z-sequence","description":"Here’s a quick one. In 1977 the magazine Popular Computing sought “problem situations for which the computer is the best (if not the only) tool for solution” and proposed the Z-sequence as a candidate “problem situation:”\r\n and  for \r\nAmong the Z-sequence’s properties, the magazine staff pointed out that “successive values seem unpredictable; that is, the values jump around, but not too wildly” and “almost every integer appears as a term in the sequence sooner or later, except for a few numbers, such as 245, 449, 569, 575, and 903.”\r\nWrite a function to find the index of the first occurrence of  (including the five numbers above) in the Popular Computing Z-sequence. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 195.817px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 97.9083px; transform-origin: 407px 97.9083px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130.958px 7.79167px; transform-origin: 130.958px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHere’s a quick one. In 1977 the magazine \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.9167px 7.79167px; transform-origin: 59.9167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ePopular Computing\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.533px 7.79167px; transform-origin: 192.533px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sought “problem situations for which the computer is the best (if not the only) tool for solution” and proposed the Z-sequence as a candidate “problem situation:”\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.9083px; text-align: left; transform-origin: 384px 10.9083px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a1 = a2 = 1\" style=\"width: 72.5px; height: 20px;\" width=\"72.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.79167px; transform-origin: 15.5583px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a_n = |2 a_{n-2} + a_{n-1} – n|\" style=\"width: 134.5px; height: 20px;\" width=\"134.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 7.79167px; transform-origin: 12.05px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n \u003e 2\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.65px 7.79167px; transform-origin: 383.65px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAmong the Z-sequence’s properties, the magazine staff pointed out that “successive values seem unpredictable; that is, the values jump around, but not too wildly” and “almost every integer appears as a term in the sequence sooner or later, except for a few numbers, such as 245, 449, 569, 575, and 903.”\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 178.775px 7.79167px; transform-origin: 178.775px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find the index of the first occurrence of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129.925px 7.79167px; transform-origin: 129.925px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (including the five numbers above) in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.8583px 7.79167px; transform-origin: 61.8583px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ePopular Computing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8417px 7.79167px; transform-origin: 40.8417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eZ-sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = findInPopCompZ(k)\r\n  y = f(k);\r\nend","test_suite":"%%\r\nassert(isequal(findInPopCompZ(1),1))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(2),4))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(4),35))\r\n    \r\n%%\r\nassert(isequal(findInPopCompZ(19),282))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(29),30))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(49),1398))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(211),241))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(245),11309))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(348),372))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(449),13409))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(569),19434))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(575),22350))\r\n    \r\n%%\r\nassert(isequal(findInPopCompZ(903),18057))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(3347),74105))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(3491),128405))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(3690),4083))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(4250),199563))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(7431),8346))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(7488),299263))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(9735),390685))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(9792),391799))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(9851),1562345))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(findInPopCompZ(4474)),15458))\r\n\r\n%%\r\nfiletext = fileread('findInPopCompZ.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-11T03:26:33.000Z","updated_at":"2026-01-14T15:14:04.000Z","published_at":"2021-07-11T03:30:22.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere’s a quick one. In 1977 the magazine \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePopular Computing\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sought “problem situations for which the computer is the best (if not the only) tool for solution” and proposed the Z-sequence as a candidate “problem situation:”\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a1 = a2 = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_1 = a_2 = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a_n = |2 a_{n-2} + a_{n-1} – n|\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_n = |2 a_{n-2} + a_{n-1} – n|\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n \u0026gt; 2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \u0026gt; 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAmong the Z-sequence’s properties, the magazine staff pointed out that “successive values seem unpredictable; that is, the values jump around, but not too wildly” and “almost every integer appears as a term in the sequence sooner or later, except for a few numbers, such as 245, 449, 569, 575, and 903.”\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find the index of the first occurrence of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (including the five numbers above) in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePopular Computing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eZ-sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55275,"title":"List the semiprimes","description":"A semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers  and  are semiprimes, but  and  are not. The semiprimes appear in three of Ramon Villamangca’s “Easy Sequences”: Cody Problems 52859, 52990, and 53740. \r\nWrite a function to list the semiprime numbers less than or equal to the input number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 297.167px 8px; transform-origin: 297.167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"6 = 2x3\" style=\"width: 60.5px; height: 18px;\" width=\"60.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"9 = 3x3\" style=\"width: 60.5px; height: 18px;\" width=\"60.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are semiprimes, but \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKgAAAAkCAYAAAAdOXEXAAAFeUlEQVR4Xu1aN8sWTRR93x9g9geIobBSMDVaKBhQsBJUtLAQTGAlKoqdfsHCwsIAloKKtopaKKgIRrSyMJRWhp+g58BeGJYJ984G58FZuDxhd3bunDlz08z0VL0qAgUjMF2wblW1isBUJWglQdEIVIIWPT1VuUrQyoGiEagELXp6qnJagi4DVDMauD7g8/uEQ+eO59mEjWUe9F3a6PwVn18mTH8T9jGCLsTAj0F2Qf5rQFjQ/H6Jz8MTCM5x6HwSMqc1qf/g94XCFx4n9n/I5pbun/F7H6T0hZaFfYigBOMxhETc05o4uUecVk4QSV81+oYMzgPPWEsxTluhyN2EMttw/14pCrf0yMY+RNBP6GARJDToA7h3BXIZQkta+sXVS+tzEHKnWXD0EDsgrkWlJT1d2GDo0j9CaCzOQsRSkrRHIa5Fnd+MraQhdMLeR1BayHfNCJfj871ntGvx31PIT8jcktDw6MIJ/gbZDbkZGQtvlTiec9BrE2RLgHz3HZJyAV4taD46Y+8jqJCP4wxZUHmG8c/iggDxqUJrvx7CWDp0uS4otCjbbQk+yfEQYrG6EiLtRTuNS/7R6O8zFNTJdf+3EuN0x0A8LkGsYRrb0Pu0Q79BsPcRVFjPDl9DfCuXq/oUpESX2AaKLuY5JJZEiBtiWy1BOcE3ms60OAg5maRpYl5JVFNh1K9GDy1BZXGRnPQaWpKSnIeavjQxb2fsQzGoq0gbSAGZK5uuZ9LKHL6VLgTlZC2BaMtoFpJayenTM/SfEPQEHjivbGglqZWcSjWmotiHCOoqz444cdshMyHXIYzlzhgmUpR1a3jaAfie67v+J+BrLZCrk4akQ5KTVpahFi+t9Xfng2FKypIORU7qEcU+Vgdtk1SIqo2dfMRy49suBO07GZCqxToolVNPjJF0SHISQ+mbno7hmPVKWdIhyUldo9indpJCJGXSEQraYwBJsdkKYvv5i/hDk2Bo+pFFk2M9U5Z0aHKyf8nirdbT1T1E0qHJmcQ+RVCJD5gEMDh2d2A0QbKGIH/6GU4wKxF9xNOuJWWNmL+1CVEODjLBltgz1E+bpAzjLAlRjv5J7GMEldUjRGSsw//cwnCuS8wZzBBtWIL6F5LrEXw6uSTlfU22njM2EuoFhGWuVJavfb/PYw5liFTYhwgqltPn9lyzPwl10NDkyIZE3xPgbnSwb20JSksieY4WbjZEU4+0vJvv3dk0sJSgLH2osQ8RlCUkuqbQ5LmDsFjRUrJ4a7FcC74bc3Lxcrt4CJJaiuVa3flc2/hQ/75JasI+tZMUCrxdK2HJqEvI4k0AGWbXlxBtRHtrMT/V5RjkpGFi+KApQaX0de+bsc8lKDuV4rCFoH86i2cczd2xWKlMrLyl3BTL1jV1Uu0kcwdvRcKt0whYz+yGsvVUCUqrN5/Lwj7l4kMHLNztULqBSdhNErBvQ9/Ybgsn6wnEd7DENyGaUlIfJOU7eJopVm2gLtcgqwzMSZWS+iBpNvapJCm0Fy/H7brWDg04dnpUAOJiksPXvhduwJ+rIdrtTg05pZ8uJJW2xPttAIlZ+J9lIY5Pu92ZIqd01YWknbCPlZnkQAhJuh8ihXkpD7C8cQSi3bfuxLAOjX2lk9jrtFm3hZxdSNouW8V0tyQ0WnJ2IWln7FOFejnUS8si1yN8SZ0O6sCn3puyZObqn+qARW/NLpm7xWgp9VjaSe05pbPcf4MvmqN/LnEsZTZru87YpwiqBeZvfY5nMZntWr1Ibrs+cSbZ1kCsW8a57bJ0rwTNgq02GguBStCxkK79ZCFQCZoFW200FgKVoGMhXfvJQqASNAu22mgsBCpBx0K69pOFQCVoFmy10VgIVIKOhXTtJwuB38VvnzR/zZ/+AAAAAElFTkSuQmCC\" alt=\"8 = 2x2x2\" style=\"width: 84px; height: 18px;\" width=\"84\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALcAAAAkCAYAAADLnKtyAAAG2klEQVR4Xu1bR8stRRB97weIaedKDAtxoRhBdKFgQFeiYlx8IJjXRlyZXSi4MP0BFd0qBlBQEYzoSsGAuHBlxB+g5zzmSL3+OlVPeDOXHiju3DsdqqtOV1efnnvwQL+6BXbUAgd3dFx9WN0CBzq4Owh21gId3Dvr2j6wDu6OgZ21QAf3zrq2D6wW3GfAVEdBfoX85DTbSSh/wlDnY2fdNRaXLajbFsdz4WDUb/H5+xoNnNDJ4igscjp++Bvyqn2QA/fxKPgI5AbIsabSj7jfq3As6z0K+QLyFeTEoa0H8PnGxgzL4d8LuT+wBX9/HPLMysfDCUm7Xx+g4h18vwviDVghuJb4/jY6uTzR0Z/4/dTQBylwE9hs7GTICxDOirMC41yE76nI9Tye3Tk4/iGj0O24fxFCo968ckBYO36OL+dkPLjm8RDYH0D+gLw8jOE6M54oMJZAq6MPrjYfZcrfh2dPh89T4CawOZsfDgAoQzGS06FXRDoUgBnhz48AWDOQEc8C3zHWRYsyYj8FuQOiFYdL5LUQG8nXOB4Gqe8hjNovBVbjyvrK8FsUHItaOd8ZMfMXhDpXXzFwc5bck2lIUZkz/rigJxmT4E852xr1TJT7plrb5QtyPL9BboQcls8NqtiIErPH8hof3iMnJlfdENgq9QNuuDq/5gXOggNjQP0achXkLU+/MXBfiQa+g6TyMEUy5tLnBp0pavPnlDKMeozqvNYY7eyQOJ6LC463KUvtZFXa9y7a9qxeWjlvqXQ09U8Bm+NsXUUZoBjkmKp58nXWof89KamCKdNgF6FRy5ZYh6szLtOh4ayjGRFSA2f+x+hOkJ8STJA1feVE/gSSY0U02al3Lbjt6lU7wcOU0AOQlE0VuWv1ZjuamAQ2V6tagAs3bKM2CttAqDEQM9w7MEXMTiwvuJV2fJaYff8OGpSWaLvzzU2CNQE9pYvA7d2YeQA+B7CVUtVOLjt+L8BbgM3+bL2Y/WMB9v9yHnBrQJw5d0NCjlS5ERv3gLt2FrP/0yZAu2tpq+hPDmjJW2sAPgew1eaTGN8+lqFizJ4I3gpsqaFzhQvwg2V59Dw5OWvATVBdOswi8d0xftSzubKROzv7jKFLdFClTw6xHrk8tLYdldPSnqNGc23mAD41sMXykP2x4Gjl6UsRfCywY3YjDp6FWGo2avsSuMWcHIPGQgI9zLcs+EpRzOaptWCjo61TvCBU+edw49p1ZzrSmEvjLekaA/jUwGYfexACMuTsx/D0KYDPAWxrR9t+lJYugTt0inbJiuDWqRbcKQ5c7T2GmweHL7XgLgHkSDznCsQN8WUQD2sQ09UCnAdnOhkeA7yUTQjIW4NgMcYPIcBJm/IQj1dt2tniPxEYrhPKXEdc2kgDEuC20bnTkpbBz1mHNNsTEFKFU3H1FuDUfQ5gW5uQ9n1z+KEUkEq2tABX2TmBzT6yZybeyC2lbeS1NFILW+KhoUoGXup588FCQUG7KWfRFibDawMb/cJDOW9bjNh6f8VDE3r7UXkdsvH7Phy1gttGaduoNle1bInHAGthS7wHKbWOszk2GSlSpEsA3FKZY8Btc2Dp7/FvrZ3Ccgqo+yjlseAOQWwHmIvIUih2ypka5BrYkiWArVSEDJXe/ZgzggvcYzbF4ebxU+jO/Yj3oMcLcEXu6GFgK7iV64RGtwBMvY9hl17PJuZIsyXaa+SOvrW6eN7zzrEiNTy4FxBheQGzNT9OsSIlmnCs3jbnjk7+VnCLJbgGPYSbKXHYqQ2K8vXUW4NTDHrqNuSo19Fw7tCDjv4QEnvJKqZTDd03J8BLJ84lO5bovrEAZ7D8J4Ix6cU0mFeUrYqB24JvDxXDKFSa6ZZNCVMT+9Zg66FHyeBTP7fvtvNEL3VdggfnQfa9NJ+oUANsVW0FuDaLsUM3jYusVyxIlexYArbqtwLcbk6ZMpE6tnQr+6ddkitpDNzheT4N8/6gKY8/GXFJgeXoLzmO1USVEfRUknlY6xJYMvjUz2P0Vq6P2tzYA+wxANcGX22QP/8ZcjSErAb90XI6WQvsMQC3B31sh/s7/XHmNtxzbHwPPYnDGLjpUL6If7Xx4pe4/wXyHqT2sELtENw84eTL5vxHiKeNqcHqbY8GZkSuvbLGNo0oEnt5bG89BhQe1pxt+magki9b/kNpJ7wnSLXUY1pyE4Tj4EUM8S+LpTc1DxVuzblrnd3LpS3AAxSyCl6Atdab0hcEKv9l5X2NobVek+4d3E1m65W2YIEO7i14qevYZIEO7iaz9UpbsEAH9xa81HVsskAHd5PZeqUtWKCDewte6jo2WaCDu8lsvdIWLNDBvQUvdR2bLPAfzCTmNPcpoA4AAAAASUVORK5CYII=\" alt=\"30 = 2x3x5\" style=\"width: 91.5px; height: 18px;\" width=\"91.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 205.517px 8px; transform-origin: 205.517px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are not. The semiprimes appear in three of Ramon Villamangca’s “Easy Sequences”: Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52859\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e52859\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52990\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e52990\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53740\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e53740\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.75px 8px; transform-origin: 264.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the semiprime numbers less than or equal to the input number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = semiprimes(n)\r\n  s = primes(n)/2;\r\nend","test_suite":"%%\r\nn = 100; \r\ns = semiprimes(n);\r\ns_correct = [4 6 9 10 14 15 21 22 25 26 33 34 35 38 39 46 49 51 55 57 58 62 65 69 74 77 82 85 86 87 91 93 94 95];\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\nn = 1000; \r\ns = semiprimes(n);\r\ns_correct = [4 6 9 10 14 15 21 22 25 26 33 34 35 38 39 46 49 51 55 57 58 62 65 69 74 77 82 85 86 87 91 93 94 95 106 111 115 118 119 121 122 123 129 133 134 141 142 143 145 146 155 158 159 161 166 169 177 178 183 185 187 194 201 202 203 205 206 209 213 214 215 217 218 219 221 226 235 237 247 249 253 254 259 262 265 267 274 278 287 289 291 295 298 299 301 302 303 305 309 314 319 321 323 326 327 329 334 335 339 341 346 355 358 361 362 365 371 377 381 382 386 391 393 394 395 398 403 407 411 413 415 417 422 427 437 445 446 447 451 453 454 458 466 469 471 473 478 481 482 485 489 493 497 501 502 505 511 514 515 517 519 526 527 529 533 535 537 538 542 543 545 551 553 554 559 562 565 566 573 579 581 583 586 589 591 597 611 614 622 623 626 629 633 634 635 649 655 662 667 669 671 674 679 681 685 687 689 694 695 697 698 699 703 706 707 713 717 718 721 723 731 734 737 745 746 749 753 755 758 763 766 767 771 778 779 781 785 789 791 793 794 799 802 803 807 813 815 817 818 831 835 838 841 842 843 849 851 862 865 866 869 871 878 879 886 889 893 895 898 899 901 905 913 914 917 921 922 923 926 933 934 939 943 949 951 955 958 959 961 965 973 974 979 982 985 989 993 995 998];\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\nn = 10000; \r\ns = semiprimes(n);\r\nlen_correct = 2625;\r\nsum_correct = 12736914;\r\nvar_correct = 8.447173943104530e+06;\r\nassert(isequal(length(s),len_correct) \u0026\u0026 isequal(sum(s),sum_correct) \u0026\u0026 abs(var(s)-var_correct)\u003c1e-8)\r\n\r\n%%\r\nn = 100000; \r\ns = semiprimes(n);\r\nlen_correct = 23378;\r\nsum_correct = 1138479765;\r\nvar_correct = 8.471797671132822e+08;\r\nassert(isequal(length(s),len_correct) \u0026\u0026 isequal(sum(s),sum_correct) \u0026\u0026 abs(var(s)-var_correct)\u003c1e-6)\r\n\r\n%%\r\nn = 800000; \r\ns = semiprimes(n);\r\nlen_correct = 169660;\r\nsum_correct = 66262251604;\r\nvar_correct = 5.417425253731966e+10;\r\nassert(isequal(length(s),len_correct) \u0026\u0026 isequal(sum(s),sum_correct) \u0026\u0026 abs(var(s)-var_correct)\u003c1e-4)\r\n\r\n%%\r\nfiletext = fileread('semiprimes.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-08-02T01:42:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-02T01:34:03.000Z","updated_at":"2025-08-03T17:11:25.000Z","published_at":"2022-08-02T01:42:35.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"6 = 2x3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6 = 2\\\\times 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"9 = 3x3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e9 = 3 \\\\times 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are semiprimes, but \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"8 = 2x2x2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e8 = 2\\\\times2 \\\\times 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"30 = 2x3x5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e30 = 2\\\\times 3 \\\\times 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are not. The semiprimes appear in three of Ramon Villamangca’s “Easy Sequences”: Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52859\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e52859\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52990\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e52990\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53740\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e53740\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list the semiprime numbers less than or equal to the input number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42647,"title":"Recursion - Fun","description":" Generate the first k terms in the sequence a(n) define recursively by \r\n\r\n a(n+1)=p*a(n)+(1+a(n)) with p=0.9 and a(1)=0.5\r\n\r\nTest Case\r\n\r\n    n = 2;\r\n    a = [a(1) a(2)] = [0.5000    1.9500]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 163.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 81.7333px; transform-origin: 407px 81.7333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 81.7333px; transform-origin: 404px 81.7333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 284px 8.5px; tab-size: 4; transform-origin: 284px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 40px 8.5px; transform-origin: 40px 8.5px; \"\u003e Generate \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 244px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 244px 8.5px; \"\u003ethe first k terms in the sequence a(n) define recursively by \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 188px 8.5px; tab-size: 4; transform-origin: 188px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 116px 8.5px; transform-origin: 116px 8.5px; \"\u003e a(n+1)=p*a(n)+(1+a(n)) with \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 72px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 72px 8.5px; \"\u003ep=0.9 and a(1)=0.5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 20px 8.5px; transform-origin: 20px 8.5px; \"\u003eTest \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 16px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 16px 8.5px; \"\u003eCase\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 40px 8.5px; tab-size: 4; transform-origin: 40px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    n = 2;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 160px 8.5px; tab-size: 4; transform-origin: 160px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    a = [a(1) a(2)] = [0.5000    1.9500]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function out = rec_fun(x)\r\n  p = 0.9;\r\n  out(1) = 0.5;\r\nend","test_suite":"%%)\r\nx = 1;\r\ny_correct = 0.5;\r\nassert(abs(rec_fun(x) - y_correct) \u003c 1e-4)\r\n\r\n%%\r\nx = 5;\r\ny_correct = [0.5000    1.9500    4.7050    9.9395   19.8851];\r\nassert(sum(abs(rec_fun(x) - y_correct)) \u003c 1e-4)\r\n\r\n%%\r\nx = 7;\r\ny_correct = [0.5000    1.9500    4.7050    9.9395   19.8851   38.7816   74.6850];\r\nassert(sum(abs(rec_fun(x) - y_correct)) \u003c 1e-4)\r\n\r\n%%\r\nx = 9;\r\ny_correct = [0.5000    1.9500    4.7050    9.9395   19.8851   38.7816   74.6850 142.9016  272.5130];\r\nassert(all(abs(rec_fun(x) - y_correct) \u003c 1e-4))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":7,"created_by":44015,"edited_by":223089,"edited_at":"2023-03-07T10:35:00.000Z","deleted_by":null,"deleted_at":null,"solvers_count":45,"test_suite_updated_at":"2023-03-07T10:33:48.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-10-03T06:35:03.000Z","updated_at":"2025-12-12T06:32:21.000Z","published_at":"2015-10-03T06:36:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Generate the first k terms in the sequence a(n) define recursively by \\n\\n a(n+1)=p*a(n)+(1+a(n)) with p=0.9 and a(1)=0.5\\n\\nTest Case\\n\\n    n = 2;\\n    a = [a(1) a(2)] = [0.5000    1.9500]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":1506,"title":"Maximum Intra-Vector Swaps","description":"This Challenge, based upon a contest in which Rokicki came in 2nd, is to find sequences containing 1:N that require maximum iterations prior to the value 1 appearing in the first position.\r\n\r\nThe processing rule is that positions 1 thru Vector(1) are swapped. Processing stops when Vector(1) is 1.\r\n\r\n*Example Sequences:* \r\n\r\n  [3 1 2], [2 1 3], [1 2 3] Score 2\r\n  [3 1 4 5 2][4 1 3 5 2][5 3 1 4 2][2 4 1 3 5][4 2 1 3 5][3 1 2 4 5][2 1 3 4 5][1 2 3 4 5]\r\n\r\n\r\n*Input:* n  (Integer from 1 to 31) (16 Actual Cases 2:11 13 17 19 23 29 31) \r\n\r\n*Output:* Vector of values 1:n\r\n\r\nExample:\r\n\r\nInput: 5  Output: [3 1 4 5 2]  \r\n\r\nScore: 7  \r\n\r\nA minimum cumulative score of 531 for the 17 cases is required to Pass.\r\n\r\nFinal Score = 2531 - sum(scores)\r\n\r\n*Hints:*\r\n\r\nUsage of perms for 10 or higher may cause Cody Memory/Time issues. Random subsets are suggested for n\u003e9.\r\n\r\nRequest: If Code is implemented external then please post as a block comment.\r\n\r\nFaster Code Block than fliplr:\r\n\r\n  function count=process_seq(seq)\r\n   count=0;\r\n   while seq(1)\u003e1\r\n    count=count+1;\r\n    seq(1:seq(1))=seq(seq(1):-1:1);\r\n   end\r\n  end","description_html":"\u003cp\u003eThis Challenge, based upon a contest in which Rokicki came in 2nd, is to find sequences containing 1:N that require maximum iterations prior to the value 1 appearing in the first position.\u003c/p\u003e\u003cp\u003eThe processing rule is that positions 1 thru Vector(1) are swapped. Processing stops when Vector(1) is 1.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample Sequences:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e[3 1 2], [2 1 3], [1 2 3] Score 2\r\n[3 1 4 5 2][4 1 3 5 2][5 3 1 4 2][2 4 1 3 5][4 2 1 3 5][3 1 2 4 5][2 1 3 4 5][1 2 3 4 5]\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e n  (Integer from 1 to 31) (16 Actual Cases 2:11 13 17 19 23 29 31)\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Vector of values 1:n\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003eInput: 5  Output: [3 1 4 5 2]\u003c/p\u003e\u003cp\u003eScore: 7\u003c/p\u003e\u003cp\u003eA minimum cumulative score of 531 for the 17 cases is required to Pass.\u003c/p\u003e\u003cp\u003eFinal Score = 2531 - sum(scores)\u003c/p\u003e\u003cp\u003e\u003cb\u003eHints:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eUsage of perms for 10 or higher may cause Cody Memory/Time issues. Random subsets are suggested for n\u003e9.\u003c/p\u003e\u003cp\u003eRequest: If Code is implemented external then please post as a block comment.\u003c/p\u003e\u003cp\u003eFaster Code Block than fliplr:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003efunction count=process_seq(seq)\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nend\r\n\u003c/pre\u003e","function_template":"function max_seq=find_max_swap_seq(n)\r\n max_seq=1:n;\r\n count=process_seq(max_seq);\r\nend\r\n\r\n% Suggested function for sequence performance evaluation\r\nfunction count=process_seq(seq)\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nend","test_suite":"tic\r\nfeval(@assignin,'caller','score',2000);\r\n%%\r\n% 2 1\r\nglobal cseq\r\ncseq{1}=1; % Gift answer\r\nmax_seq=find_max_swap_seq(2);\r\nassert(isequal(1:2,unique(max_seq)))\r\ncseq{2}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n% 3 2\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(3);\r\nassert(isequal(1:3,unique(max_seq)))\r\ncseq{3}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n% 4 4\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(4);\r\nassert(isequal(1:4,unique(max_seq)))\r\ncseq{4}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n% 5 7\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(5);\r\nassert(isequal(1:5,unique(max_seq)))\r\ncseq{5}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n% 6 10\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(6);\r\nassert(isequal(1:6,unique(max_seq)))\r\ncseq{6}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n% 7 16\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(7);\r\nassert(isequal(1:7,unique(max_seq)))\r\ncseq{7}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n% 8 22\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(8);\r\nassert(isequal(1:8,unique(max_seq)))\r\ncseq{8}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n% 9 30\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(9);\r\nassert(isequal(1:9,unique(max_seq)))\r\ncseq{9}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n%10 38\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(10);\r\nassert(isequal(1:10,unique(max_seq)))\r\ncseq{10}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n%11 51\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(11);\r\nassert(isequal(1:11,unique(max_seq)))\r\ncseq{11}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n%13 80 case 12\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(13);\r\nassert(isequal(1:13,unique(max_seq)))\r\ncseq{12}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n%17 159 case 13\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(17);\r\nassert(isequal(1:17,unique(max_seq)))\r\ncseq{13}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n%19 221 case 14\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(19);\r\nassert(isequal(1:19,unique(max_seq)))\r\ncseq{14}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n%23 382 case 15\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(23);\r\nassert(isequal(1:23,unique(max_seq)))\r\ncseq{15}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n%29 689 case 16\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(29);\r\nassert(isequal(1:29,unique(max_seq)))\r\ncseq{16}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\n%%\r\n%31 819 case 17\r\nglobal cseq\r\nmax_seq=find_max_swap_seq(31);\r\nassert(isequal(1:31,unique(max_seq)))\r\ncseq{17}=max_seq;\r\n seq=max_seq;\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\nfprintf('count %i\\n',count)\r\nfprintf('%i ',max_seq)\r\nfprintf('\\n')\r\ntoc\r\n%%\r\nglobal cseq\r\ntotal=0;\r\nfor i=2:17\r\n seq=cseq{i};\r\n count=0;\r\n while seq(1)\u003e1\r\n  count=count+1;\r\n  seq(1:seq(1))=seq(seq(1):-1:1);\r\n end\r\n total=total+count;\r\nend\r\n\r\n% 2531 is optimal sum\r\ntotal=sum([0 1 2 4 7 10 16 22 30 38 51 80 159 221 382 689 819])-total;\r\nassert(total\u003c2001); % Minimum performance requirement\r\n\r\ntoc\r\nfeval(@assignin,'caller','score',min(2000,total));\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-05-13T01:28:12.000Z","updated_at":"2026-04-01T14:34:03.000Z","published_at":"2013-05-13T04:01:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge, based upon a contest in which Rokicki came in 2nd, is to find sequences containing 1:N that require maximum iterations prior to the value 1 appearing in the first position.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe processing rule is that positions 1 thru Vector(1) are swapped. Processing stops when Vector(1) is 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample Sequences:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[3 1 2], [2 1 3], [1 2 3] Score 2\\n[3 1 4 5 2][4 1 3 5 2][5 3 1 4 2][2 4 1 3 5][4 2 1 3 5][3 1 2 4 5][2 1 3 4 5][1 2 3 4 5]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e n (Integer from 1 to 31) (16 Actual Cases 2:11 13 17 19 23 29 31)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Vector of values 1:n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: 5 Output: [3 1 4 5 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eScore: 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA minimum cumulative score of 531 for the 17 cases is required to Pass.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFinal Score = 2531 - sum(scores)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsage of perms for 10 or higher may cause Cody Memory/Time issues. Random subsets are suggested for n\u0026gt;9.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRequest: If Code is implemented external then please post as a block comment.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFaster Code Block than fliplr:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[function count=process_seq(seq)\\n count=0;\\n while seq(1)\u003e1\\n  count=count+1;\\n  seq(1:seq(1))=seq(seq(1):-1:1);\\n end\\nend]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42715,"title":" Throw common elements of two vector arrays in sorted manner","description":"\r\nThrow common elements as output in sorted manner (acending order) of two given input vector arrays","description_html":"\u003cp\u003eThrow common elements as output in sorted manner (acending order) of two given input vector arrays\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nA = [1 2 3 4 5 6 7 8];\r\nB = [4 5 6 6 7 0 12 34];\r\ny_correct = [7 6 5 4];\r\nassert(isequal(your_fcn_name(A,B),y_correct))\r\n\r\n%%\r\nA = [1 2 3 4 5 6 71 8];\r\nB = [4 5 6 6 7 0 12 34];\r\ny_correct = [6 5 4];\r\nassert(isequal(your_fcn_name(A,B),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":46868,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":74,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-01-15T10:10:48.000Z","updated_at":"2026-02-28T08:11:04.000Z","published_at":"2016-01-15T10:17:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThrow common elements as output in sorted manner (acending order) of two given input vector arrays\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60286,"title":"Hofstadter Q sequence","description":"The Hofstadter Q sequence is defined as follows:\r\n\r\nThe first elements of the sequence are 1, 1, 2, 3, 3, 4, 5, 5, 6, 6.\r\nWrite a function to compute  for a given n.\r\nSee https://oeis.org/A005185","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 170.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343.5px 85.45px; transform-origin: 343.5px 85.45px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.5px; text-align: left; transform-origin: 320.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Hofstadter Q sequence is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 49.4px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 24.7px; text-align: left; transform-origin: 320.5px 24.7px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-19px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"164.5\" height=\"49.5\" style=\"width: 164.5px; height: 49.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.5px; text-align: left; transform-origin: 320.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first elements of the sequence are 1, 1, 2, 3, 3, 4, 5, 5, 6, 6.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 11.25px; text-align: left; transform-origin: 320.5px 11.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003efor a given\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.5px; text-align: left; transform-origin: 320.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSee \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A005185\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://oeis.org/A005185\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function q = Q_sequence(n)\r\n\r\nend","test_suite":"all_glo = [1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 6, 8, 8, 8, 10, 9, 10, 11, 11, 12, 12, 12, 12, 16, 14, 14, 16, 16, 16, 16, 20, 17, 17, 20, 21, 19, 20, 22, 21, 22, 23, 23, 24, 24, 24, 24, 24, 32, 24, 25, 30, 28, 26, 30, 30, 28, 32, 30, 32, 32, 32, 32, 40, 33, 31, 38, 35, 33, 39, 40, 37, 38, 40, 39, 40, 39, 42, 40, 41, 43, 44, 43, 43, 46, 44, 45, 47, 47, 46, 48, 48, 48, 48, 48, 48, 64, 41, 52, 54, 56, 48, 54, 54, 50, 60, 52, 54, 58, 60, 53, 60, 60, 52, 62, 66, 55, 62, 68, 62, 58, 72, 58, 61, 78, 57, 71, 68, 64, 63, 73, 63, 71, 72, 72, 80, 61, 71, 77, 65, 80, 71, 69, 77, 75, 73, 77, 79, 76, 80, 79, 75, 82, 77, 80, 80, 78, 83, 83, 78, 85, 82, 85, 84, 84, 88, 83, 87, 88, 87, 86, 90, 88, 87, 92, 90, 91, 92, 92, 94, 92, 93, 94, 94, 96, 94, 96, 96, 96, 96, 96, 96, 128, 72, 96, 115, 100, 84, 114, 110, 93, 106, 124, 82, 101, 111, 108, 118, 104, 108, 106, 114, 104, 114, 109, 100, 109, 120, 112, 108, 118, 106, 105, 130, 110, 114, 115, 112, 107, 120, 114, 122, 121, 120, 114, 138, 110, 122, 119, 120, 130];\r\nn = randi([90,numel(all_glo)]) \r\ny_correct = all_glo(n)\r\n\r\n%%\r\n% Only for this random test, n and y_correct are displayed but their definition is hidden.\r\nn\r\ny_obtained = Q_sequence(n)\r\ny_correct\r\nassert(isequal(y_obtained,y_correct));\r\n\r\n\r\n%%\r\nn = 73\r\ny_obtained = Q_sequence(n)\r\ny_correct = 40\r\nassert(isequal(y_obtained,y_correct));\r\n\r\n%%\r\nyy_correct = [1,1,2,3,3,4,5,5,6,6,6,8,8,8,10,9,10,11,11,12,12];\r\nfor n = 1:numel(yy_correct)\r\n    y_obtained = Q_sequence(n);\r\n    y_correct = yy_correct(n);\r\n    assert(isequal(y_obtained,y_correct));\r\nend","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":208445,"edited_by":208445,"edited_at":"2024-06-09T15:57:38.000Z","deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":"2024-05-11T18:02:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-11T17:54:45.000Z","updated_at":"2026-03-01T15:18:23.000Z","published_at":"2024-05-11T18:02:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Hofstadter Q sequence is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$$\\\\begin{cases}\\nQ_1 = Q_2 = 1\\\\\\\\\\nQ_n = Q_{n-Q_{n-1}}+Q_{n-Q_{n-2}}\\n\\\\end{cases}$$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first elements of the sequence are 1, 1, 2, 3, 3, 4, 5, 5, 6, 6.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003efor a given\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A005185\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://oeis.org/A005185\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1655,"title":"Sum of first n positive integers","description":"Given n, find the sum of first n positive integers\r\nExample: If n=10, then x=1,2,3,4,5,6,7,8,9,10. The sum of these terms is 55","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 148px 8px; transform-origin: 148px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven n, find the sum of first n positive integers\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 236.5px 8px; transform-origin: 236.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample: If n=10, then x=1,2,3,4,5,6,7,8,9,10. The sum of these terms is 55\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = summation(n)\r\n y=n;\r\nend","test_suite":"%%\r\nn = 10;\r\ny = 55;\r\nassert(isequal(summation(n),y))\r\n%%\r\nn = 0;\r\ny = 0;\r\nassert(isequal(summation(n),y))\r\n%%\r\nn = 17;\r\ny = 153;\r\nassert(isequal(summation(n),y))\r\n%%\r\nn = 100;\r\ny = 5050;\r\nassert(isequal(summation(n),y))\r\n%%\r\nn = 1000;\r\ny = 500500;\r\nassert(isequal(summation(n),y))","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":14636,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":622,"test_suite_updated_at":"2021-09-27T15:20:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-19T05:26:57.000Z","updated_at":"2026-02-06T18:34:50.000Z","published_at":"2013-06-19T05:30:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven n, find the sum of first n positive integers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: If n=10, then x=1,2,3,4,5,6,7,8,9,10. The sum of these terms is 55\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44818,"title":"Add consecutive integer numbers","description":"Given consecutive numbers, add the numbers *without using the sum command in MATLAB.*","description_html":"\u003cp\u003eGiven consecutive numbers, add the numbers \u003cb\u003ewithout using the sum command in MATLAB.\u003c/b\u003e\u003c/p\u003e","function_template":"function y = add_consecutive_integers(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(add_consecutive_integers(x),y_correct))\r\n\r\n%%\r\nx = 1:10;\r\ny_correct = sum(x);\r\nassert(isequal(add_consecutive_integers(x),y_correct))\r\n\r\n%%\r\nx = 5:10;\r\ny_correct = sum(x);\r\nassert(isequal(add_consecutive_integers(x),y_correct))\r\n\r\n%%\r\nx = 50:100;\r\ny_correct = sum(x);\r\nassert(isequal(add_consecutive_integers(x),y_correct))\r\n\r\n\r\n%% \r\nassessFunctionAbsence('sum','Filename','add_consecutive_integers')","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":265425,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":58,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":677,"created_at":"2019-01-04T22:24:50.000Z","updated_at":"2026-02-17T21:08:18.000Z","published_at":"2019-01-04T22:25:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven consecutive numbers, add the numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewithout using the sum command in MATLAB.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":48005,"title":"number play","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 111px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 55.5px; transform-origin: 407px 55.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFrom the sequence 3,8,13,18,23,28,33,38.....\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eif the input n=2 output should be y=[13 18]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                  n=6;y=[53 58]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = seq(n)\r\n  y = ;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = [3 8];\r\nassert(isequal(seq(n),y_correct))\r\n%%\r\nn = 5;\r\ny_correct = [43 48];\r\nassert(isequal(seq(n),y_correct))\r\n%%\r\nn = 200;\r\ny_correct = [1993 1998];\r\nassert(isequal(seq(n),y_correct))\r\n%%\r\nn = 501;\r\ny_correct = [5003 5008];\r\nassert(isequal(seq(n),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":628208,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":51,"test_suite_updated_at":"2020-12-17T06:48:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-17T06:40:21.000Z","updated_at":"2026-02-19T15:40:04.000Z","published_at":"2020-12-17T06:48:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFrom the sequence 3,8,13,18,23,28,33,38.....\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eif the input n=2 output should be y=[13 18]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                  n=6;y=[53 58]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61168,"title":"Find record values in a sequence","description":"Write a function to find the record values in a sequence—that is, the largest values seen since the start. For example, if the sequence is\r\n1, 2, 0, 4, 5, 3, 7, 8, 6, 10, 11, 9, 13, 14, 12, 16\r\nthen the function should return\r\n1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 66px; transform-origin: 408px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find the record values in a sequence—that is, the largest values seen since the start. For example, if the sequence is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e1, 2, 0, 4, 5, 3, 7, 8, 6, 10, 11, 9, 13, 14, 12, 16\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen the function should return\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = records(x)\r\n  y = sort(x,'descending');\r\nend","test_suite":"%%  Example (tersum n+n)\r\nx = [1 2 0 4 5 3 7 8 6 10 11 9 13 14 12 16];\r\ny = records(x);\r\ny_correct = [1 2 4 5 7 8 10 11 13 14 16];\r\nassert(isequal(y,y_correct))\r\n\r\n%%  Prime gaps\r\nx = [1 2 2 4 2 4 2 4 6 2 6 4 2 4 6 6 2 6 4 2 6 4 6 8 4 2 4 2 4 14 4 6 2 10 2 6 6 4 6 6 2 10 2 4 2 12 12 4 2 4 6 2 10 6 6 6 2 6 4 2 10 14 4 2 4 14 6 10 2 4 6 8 6 6 4 6 8 4 8 10 2 10 2 6 4 6 8 4 2 4 12 8 4 8 4 6 12 2 18 6];\r\ny = records(x);\r\ny_correct = [1 2 4 6 8 14 18];\r\nassert(isequal(y,y_correct))\r\n\r\n%%  Numbers of divisors\r\nx = [1 2 2 3 2 4 2 4 3 4 2 6 2 4 4 5 2 6 2 6 4 4 2 8 3 4 4 6 2 8 2 6 4 4 4 9 2 4 4 8 2 8 2 6 6 4 2 10 3 6 4 6 2 8 4 8 4 4 2 12 2 4 6 7 4 8 2 6 4 8 2 12 2 4 6 6 4 8 2 10 5 4 2 12 4 4 4 8 2 12 4 6 4 4 4 12 2 6 6 9];\r\ny = records(x);\r\ny_correct = [1 2 3 4 6 8 9 10 12];\r\nassert(isequal(y,y_correct))\r\n\r\n%%  Length of the period of the continued fraction of (1+sqrt(n))/2\r\nx = [0 2 2 0 1 4 4 4 0 2 2 2 1 4 2 0 3 6 6 4 2 6 4 4 0 2 2 4 1 2 8 4 4 4 2 0 3 6 6 8 5 4 10 6 2 8 4 4 0 2 2 4 1 6 4 2 6 6 6 4 3 4 2 0 3 6 10 6 4 6 8 4 9 6 4 8 2 4 4 4 0 2 2 2 1 6 2 8 7 2 8 8 2 12 4 8 9 4 2 0];\r\ny = records(x);\r\ny_correct = [0 2 4 6 8 10 12];\r\nassert(isequal(y,y_correct))\r\n\r\n%%  Numbers of ways n can be properly factored\r\nx = [0 0 0 1 0 1 0 2 1 1 0 3 0 1 1 4 0 3 0 3 1 1 0 6 1 1 2 3 0 4 0 6 1 1 1 8 0 1 1 6 0 4 0 3 3 1 0 11 1 3 1 3 0 6 1 6 1 1 0 10 0 1 3 10 1 4 0 3 1 4 0 15 0 1 3 3 1 4 0 11 4 1 0 10 1 1 1 6 0 10 1 3 1 1 1 18 0 3 3 8];\r\ny = records(x);\r\ny_correct = [0 1 2 3 4 6 8 11 15 18];   \r\nassert(isequal(y,y_correct))\r\n\r\n%%  Numbers of ways n can be properly factored\r\nx = [1 1 1 2 1 1 1 3 2 1 1 2 1 1 1 4 1 2 1 2 1 1 1 3 2 1 3 2 1 1 1 5 1 1 1 4 1 1 1 3 1 1 1 2 2 1 1 4 2 2 1 2 1 3 1 3 1 1 1 2 1 1 2 6 1 1 1 2 1 1 1 6 1 1 2 2 1 1 1 4 4 1 1 2 1 1 1 3 1 2 1 2 1 1 1 5 1 2 2 4 1 1 1 3 1 1 1 6 1 1 1 4 1 1 1 2 2 1 1 3 2 1 1 2 3 2 1 7 1 1 1 2 1 1 3 3 1 1 1 2 1 1 1 8 1 1 2 2 1 2 1 3 2 1 1 2 1 1 1 5 1 4 1 2 1 1 1 3 2 1 2 2 1 1 2 4 1 1 1 4 1 1 1 3 1 1 1 2 3 1 1 6 1 1 1 4 1 2 1 6];\r\ny = records(x);\r\ny_correct = 1:8;   \r\nassert(isequal(y,y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2026-01-20T02:33:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-20T02:33:28.000Z","updated_at":"2026-02-18T21:58:32.000Z","published_at":"2026-01-20T02:33:49.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find the record values in a sequence—that is, the largest values seen since the start. For example, if the sequence is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 0, 4, 5, 3, 7, 8, 6, 10, 11, 9, 13, 14, 12, 16\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen the function should return\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44225,"title":"Sum of self power series","description":"The series, 1^1,2^2,3^3,4^4,....\r\n\r\nFind the sum of such series when x terms are given.","description_html":"\u003cp\u003eThe series, 1^1,2^2,3^3,4^4,....\u003c/p\u003e\u003cp\u003eFind the sum of such series when x terms are given.\u003c/p\u003e","function_template":"function y = sumofseries(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(sumofseries(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 5;\r\nassert(isequal(sumofseries(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 288;\r\nassert(isequal(sumofseries(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":134801,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":81,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-05-25T05:40:41.000Z","updated_at":"2026-03-10T15:08:41.000Z","published_at":"2017-05-25T05:40:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe series, 1^1,2^2,3^3,4^4,....\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the sum of such series when x terms are given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42833,"title":"Return the sequence element I","description":"Given a positive integer, x, return a positive integer, y, which is the xth term in the sequence [1 2 2 3 3 3...], in which one instance of the number 1 is followed by two instances of the number 2, followed by three instances of the number 3, and so on.\r\n\r\nExample 1:\r\n\r\nx = 5\r\n\r\ny = 3\r\n\r\nExample 2:\r\n\r\nx = 105\r\n\r\ny = 14","description_html":"\u003cp\u003eGiven a positive integer, x, return a positive integer, y, which is the xth term in the sequence [1 2 2 3 3 3...], in which one instance of the number 1 is followed by two instances of the number 2, followed by three instances of the number 3, and so on.\u003c/p\u003e\u003cp\u003eExample 1:\u003c/p\u003e\u003cp\u003ex = 5\u003c/p\u003e\u003cp\u003ey = 3\u003c/p\u003e\u003cp\u003eExample 2:\u003c/p\u003e\u003cp\u003ex = 105\u003c/p\u003e\u003cp\u003ey = 14\u003c/p\u003e","function_template":"function y = seqelem(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('seqelem.m');\r\nassert(isempty(strfind(filetext,'feval')))\r\nassert(isempty(strfind(filetext,'polyval')))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 3;\r\nassert(isequal(seqelem(x),y_correct))\r\n\r\n%%\r\nx = 105;\r\ny_correct = 14;\r\nassert(isequal(seqelem(x),y_correct))\r\n\r\n%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(seqelem(x),y_correct))\r\n\r\n%%\r\nx = 5040;\r\ny_correct = 100;\r\nassert(isequal(seqelem(x),y_correct))\r\n\r\n%%\r\nx = 96669;\r\ny_correct = 440;\r\nassert(isequal(seqelem(x),y_correct))\r\n\r\n%%\r\nx = 9999991;\r\ny_correct = 4472;\r\nassert(isequal(seqelem(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-26T15:10:19.000Z","updated_at":"2026-02-28T08:12:49.000Z","published_at":"2016-04-26T15:10:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a positive integer, x, return a positive integer, y, which is the xth term in the sequence [1 2 2 3 3 3...], in which one instance of the number 1 is followed by two instances of the number 2, followed by three instances of the number 3, and so on.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 105\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = 14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":48030,"title":"Find the Pattern 3","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 171px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 85.5px; transform-origin: 407px 85.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the pattern for the following sequence:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(2) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(11) = 143\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(15) = 255\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(17) = 323\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCreate a function which satisfies the pattern shown above.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pat(x)\r\n  y = x/2;\r\nend","test_suite":"%%\r\nx = 2;\r\ny_correct = 8;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 11;\r\ny_correct = 143;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 17;\r\ny_correct = 323;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 212;\r\ny_correct = 45368;\r\nassert(isequal(pat(x),y_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":251,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-17T19:27:48.000Z","updated_at":"2026-03-20T14:59:15.000Z","published_at":"2020-12-17T19:27:48.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the pattern for the following sequence:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(2) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(11) = 143\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(15) = 255\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(17) = 323\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a function which satisfies the pattern shown above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43684,"title":"0, 2, 0, -2, 0, 2, 0, -2, ...","description":"Generate the first n terms of a periodic sequence defined as\r\n\r\n  f(x) = 0, 2, 0, -2, 0, 2, 0, -2, ..., for x = 1, 2, 3, 4, 5, 6, 7, 8, ...","description_html":"\u003cp\u003eGenerate the first n terms of a periodic sequence defined as\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ef(x) = 0, 2, 0, -2, 0, 2, 0, -2, ..., for x = 1, 2, 3, 4, 5, 6, 7, 8, ...\r\n\u003c/pre\u003e","function_template":"function y = seq(n)\r\n  y = n;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = [0];\r\nassert(isequal(seq(n),y_correct))\r\n\r\n%%\r\nn = 4\r\ny_correct = [0, 2, 0, -2];\r\nassert(isequal(seq(n),y_correct))\r\n\r\n%%\r\nn = 5\r\ny_correct = [0, 2, 0, -2, 0];\r\nassert(isequal(seq(n),y_correct))\r\n\r\n%%\r\nn = 8\r\ny_correct = [0, 2, 0, -2, 0, 2, 0, -2];\r\nassert(isequal(seq(n),y_correct))\r\n\r\n%%\r\nn = 25\r\ny_correct = [0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0];\r\nassert(isequal(seq(n),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":81,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-11-26T20:23:48.000Z","updated_at":"2026-02-26T12:18:36.000Z","published_at":"2016-11-26T20:25:21.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGenerate the first n terms of a periodic sequence defined as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[f(x) = 0, 2, 0, -2, 0, 2, 0, -2, ..., for x = 1, 2, 3, 4, 5, 6, 7, 8, ...]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":48065,"title":"Find the Pattern 10","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 171px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 85.5px; transform-origin: 407px 85.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the pattern for the following sequence:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(1) = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(2) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(3) = 25\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(7) = 169\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCreate a function which satisfies the pattern shown above.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pat(x)\r\n  y = x+tan(x);\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 2;\r\ny_correct = 9;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 5;\r\ny_correct = 81;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 11;\r\ny_correct = 441;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 7;\r\ny_correct = 169;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 25;\r\ny_correct = 2401;\r\nassert(isequal(pat(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":244,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-17T20:13:51.000Z","updated_at":"2026-03-20T15:10:27.000Z","published_at":"2020-12-17T20:13:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the pattern for the following sequence:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(2) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(3) = 25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(7) = 169\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a function which satisfies the pattern shown above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54770,"title":"Count the peaceful queens","description":"In a 5x5 chessboard with a queen of one color (white, say) on the perimeter, one can place 12 black queens on the board such that none of the black queens can attack the white one (or vice versa). \r\nWrite a function that returns the number of queens that cannot attack a queen of the other color placed anywhere on the perimeter of an x chessboard.  \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 328.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 164.35px; transform-origin: 407px 164.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.1833px 8px; transform-origin: 85.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn a 5x5 chessboard with a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Queen_(chess)#Placement_and_movement\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003equeen\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 272.283px 8px; transform-origin: 272.283px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of one color (white, say) on the perimeter, one can place 12 black queens on the board such that none of the black queens can attack the white one (or vice versa). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 372.883px 8px; transform-origin: 372.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the number of queens that cannot attack a queen of the other color placed anywhere on the perimeter of an \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.5px 8px; transform-origin: 3.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.0083px 8px; transform-origin: 42.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e chessboard. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 226.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 113.35px; text-align: left; transform-origin: 384px 113.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 764px;height: 221px\" 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\" data-image-state=\"image-loaded\" width=\"764\" height=\"221\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = peacefulQueens(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 5;\r\nassert(isequal(peacefulQueens(n),12))\r\n\r\n%%\r\nn = 8;\r\nassert(isequal(peacefulQueens(n),42))\r\n\r\n%%\r\nn = 64;\r\nassert(isequal(peacefulQueens(n),3906))\r\n\r\n%%\r\nn = 4096;\r\nassert(isequal(peacefulQueens(n),16764930))\r\n\r\n%%\r\nn = 262144;\r\nassert(isequal(peacefulQueens(n),68718690306))\r\n\r\n%%\r\nn = 2097152;\r\nassert(isequal(peacefulQueens(n),4398040219650))\r\n\r\n%%\r\nn = 16777216;\r\nassert(isequal(peacefulQueens(n),281474926379010))\r\n\r\n%%\r\nm = randi(1000)+4;\r\ny = sum(arrayfun(@peacefulQueens,3:m));\r\nassert(isequal(y,polyval([1 3 2 0],m-2)/3))\r\n\r\n%%\r\nfiletext = fileread('peacefulQueens.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-07-02T17:52:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":76,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-07-02T02:16:14.000Z","updated_at":"2026-01-26T15:48:57.000Z","published_at":"2022-07-02T02:17:02.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a 5x5 chessboard with a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Queen_(chess)#Placement_and_movement\\\"\u003e\u003cw:r\u003e\u003cw:t\u003equeen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of one color (white, say) on the perimeter, one can place 12 black queens on the board such that none of the black queens can attack the white one (or vice versa). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the number of queens that cannot attack a queen of the other color placed anywhere on the perimeter of an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54675,"title":"Define an arithmetic sequence","description":"Given three numbers n, a, and d, define an arithmetic sequence of n terms with a being the initial term of the sequence and d being the common difference of the sequence. If n = 0, then return an empty array since there would be no terms in the sequence.\r\nExamples:\r\nInput  [n,a,d] = deal(10,5,2)\r\nOutput seq = [5 7 9 11 13 15 17 19 21 23]\r\n\r\nInput  [n,a,d] = deal(5,2,-3)\r\nOutput seq = [2 -1 -4 -7 -10]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 225.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 112.875px; transform-origin: 407px 112.875px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven three numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, define an arithmetic sequence of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e terms with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e being the initial term of the sequence and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e being the common difference of the sequence. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e = 0, then return an empty array since there would be no terms in the sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4375px; transform-origin: 404px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eInput  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003e[n,a,d] = deal(10,5,2)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eseq = [5 7 9 11 13 15 17 19 21 23]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.875px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4375px; transform-origin: 404px 20.4375px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eInput  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003e[n,a,d] = deal(5,2,-3)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eseq = [2 -1 -4 -7 -10]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function seq = arithSequence(n,a,d)\r\n    seq = [n a d];\r\nend","test_suite":"%%\r\n[n,a,d] = deal(10,5,2);\r\nseq_correct = [5 7 9 11 13 15 17 19 21 23];\r\nassert(isequal(arithSequence(n,a,d),seq_correct))\r\n%%\r\n[n,a,d] = deal(5,2,-3);\r\nseq_correct = [2 -1 -4 -7 -10];\r\nassert(isequal(arithSequence(n,a,d),seq_correct))\r\n%%\r\n[n,a,d] = deal(7,3,0.5);\r\nseq_correct = [3 3.5 4 4.5 5 5.5 6];\r\nassert(isequal(arithSequence(n,a,d),seq_correct))\r\n%%\r\n[n,a,d] = deal(0, 1, 2);\r\nassert(isempty(arithSequence(n,a,d)))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":792819,"edited_by":792819,"edited_at":"2022-05-24T21:17:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-05-24T21:17:06.000Z","updated_at":"2026-03-05T13:32:48.000Z","published_at":"2022-05-24T21:17:27.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven three numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, define an arithmetic sequence of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e terms with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e being the initial term of the sequence and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e being the common difference of the sequence. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e = 0, then return an empty array since there would be no terms in the sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Input  [n,a,d] = deal(10,5,2)\\nOutput seq = [5 7 9 11 13 15 17 19 21 23]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Input  [n,a,d] = deal(5,2,-3)\\nOutput seq = [2 -1 -4 -7 -10]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":48020,"title":"Find the Pattern 1","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 141px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 70.5px; transform-origin: 407px 70.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the pattern for the following sequence:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(1) = 10\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(3) = 16\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(7) = 28\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCreate a function which satisfies the pattern shown above.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pat(x)\r\n  y = sqrt(x)+2*x^2;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 10;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 3;\r\ny_correct = 16;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 7;\r\ny_correct = 28;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 11;\r\ny_correct = 40;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 20;\r\ny_correct = 67;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 99;\r\ny_correct = 304;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 12345;\r\ny_correct = 37042;\r\nassert(isequal(pat(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":290,"test_suite_updated_at":"2020-12-17T18:55:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-17T18:47:37.000Z","updated_at":"2026-03-20T14:58:29.000Z","published_at":"2020-12-17T18:55:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the pattern for the following sequence:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(1) = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(3) = 16\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(7) = 28\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a function which satisfies the pattern shown above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47255,"title":"Find Logic 8","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 191.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 95.8333px; transform-origin: 174px 95.8333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) =  3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 15\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 0;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 8;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 24\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":467,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-04T07:53:36.000Z","updated_at":"2026-02-14T07:11:40.000Z","published_at":"2020-11-04T07:53:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) =  3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 15\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45254,"title":"Tribonacci Sequence","description":"Generate the tribonacci sequence upto n","description_html":"\u003cp\u003eGenerate the tribonacci sequence upto n\u003c/p\u003e","function_template":"function t = tribonacci(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nn = 5;\r\ny_correct = [0,0,1,1,2];\r\nassert(isequal(tribonacci(n),y_correct))\r\n%%\r\nn = 11;\r\ny_correct = [0     0     1     1     2     4     7    13    24    44  81  ];\r\nassert(isequal(tribonacci(n),y_correct))\r\n%%\r\nn = 21;\r\ny_correct = [0\t0\t1\t1\t2\t4\t7\t13\t24\t44\t81\t149\t274\t504\t927\t1705\t3136\t5768\t10609\t19513\t35890];\r\nassert(isequal(tribonacci(n),y_correct))\r\n%%\r\nn = 30;\r\ny_correct =[ 0\t0\t1\t1\t2\t4\t7\t13\t24\t44\t81\t149\t274\t504\t927\t1705\t3136\t5768\t10609\t19513\t35890\t66012\t121415\t223317\t410744\t755476\t1389537\t2555757\t4700770\t8646064];\r\nassert(isequal(tribonacci(n),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":45,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-03T19:15:46.000Z","updated_at":"2025-06-14T03:37:34.000Z","published_at":"2020-01-03T19:19:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGenerate the tribonacci sequence upto n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60306,"title":"Add non-triangular numbers","description":"The nth triangular number is the sum of the first n positive integers. The sequence of triangular numbers starts 1, 3, 6, 10, 15, and 21. These numbers are involved in Cody Problems 5, 291, 44289, 44334, 44732, 55680, 55695, 55705, 55710, and 55715, for example. \r\nWrite a function to return the sum of the non-triangular numbers between the nth and (n+1)st triangular numbers. For example, if n = 3, then the function should return 7+8+9 = 24. Beware the banned functions.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377.658px 8px; transform-origin: 377.658px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe nth triangular number is the sum of the first n positive integers. The sequence of triangular numbers starts 1, 3, 6, 10, 15, and 21. These numbers are involved in Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/5\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e5\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/291\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e291\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44289\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44289\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44334\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44334\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44732\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44732\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55680\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55680\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55695\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55695\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55705\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55705\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55710\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55710\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.775px 8px; transform-origin: 16.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55715\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55715\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 8px; transform-origin: 44.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, for example. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 362.975px 8px; transform-origin: 362.975px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to return the sum of the non-triangular numbers between the nth and (n+1)st triangular numbers. For example, if n = 3, then the function should return 7+8+9 = 24. Beware the banned functions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = addNonTriangular(n)\r\n  y = sum(tril(n)+1:triu(n)-1);\r\nend","test_suite":"%%\r\nassert(isequal(addNonTriangular(1),2))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(2),9))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(3),24))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(4),50))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(44),44550))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(92),397854))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(267),9588504))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(389),29583450))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(461),49198842))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(556),86249222))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(632),126617724))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(709),178703450))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(878),339189399))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(913),381358274))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(1255),989903840))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(6534),139521237075))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(14342),1475229944979))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(78422),241154195453019))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(256347),8422831459859544))\r\n\r\n%%\r\nassert(isequal(addNonTriangular(addNonTriangular(2429)/(3^10*347)),21560175))\r\n\r\n%%\r\ns = [0 1 4 9 6 5 6 9 4 1];\r\nn = randi(1000);\r\nm = n:n+2;\r\nd = num2str((2*arrayfun(@addNonTriangular,m)./m)')-'0';\r\nd1 = d(:,end)';\r\nassert(~isempty(strfind([s s],d1)))\r\n\r\n%%\r\nfiletext = fileread('addNonTriangular.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp') || contains(filetext,'sum') || contains(filetext,'trace')  || contains(filetext,'ones')  || contains(filetext,'eye'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-14T01:38:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-14T01:37:57.000Z","updated_at":"2026-03-04T14:14:54.000Z","published_at":"2024-05-14T01:38:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe nth triangular number is the sum of the first n positive integers. The sequence of triangular numbers starts 1, 3, 6, 10, 15, and 21. These numbers are involved in Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/5\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/291\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e291\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44289\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44289\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44334\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44334\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44732\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44732\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55680\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55680\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55695\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55695\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55705\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55705\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55710\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55710\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55715\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55715\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, for example. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to return the sum of the non-triangular numbers between the nth and (n+1)st triangular numbers. For example, if n = 3, then the function should return 7+8+9 = 24. Beware the banned functions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44543,"title":"Normie Function","description":"So, I built a function and gave it a name- _Normie_.\r\n*Find the nth term of Normie function:*\r\n_f(n)= 1*f(n-1)+ 2*f(n-3)+ 3_ , *when n\u003e3* and _0_ , *when n\u003c=3*.","description_html":"\u003cp\u003eSo, I built a function and gave it a name- \u003ci\u003eNormie\u003c/i\u003e. \u003cb\u003eFind the nth term of Normie function:\u003c/b\u003e \u003ci\u003ef(n)= 1*f(n-1)+ 2*f(n-3)+ 3\u003c/i\u003e , \u003cb\u003ewhen n\u0026gt;3\u003c/b\u003e and \u003ci\u003e0\u003c/i\u003e , \u003cb\u003ewhen n\u0026lt;=3\u003c/b\u003e.\u003c/p\u003e","function_template":"function y = nth_term(n)\r\n  y = n;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = 0;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 2;\r\ny_correct = 0;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 3;\r\ny_correct = 0;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 4;\r\ny_correct = 3;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 5;\r\ny_correct = 6;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 10;\r\ny_correct = 93;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 11;\r\ny_correct = 162;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 20;\r\ny_correct = 18753;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 35;\r\ny_correct = 51651090;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 50;\r\ny_correct = 142236278205;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 70;\r\ny_correct = 5490159117130629;\r\nassert(isequal(nth_term(n),y_correct))\r\n%%\r\nn = 75;\r\ny_correct = 76953534045721408;\r\nassert(isequal(nth_term(n),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":104442,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2018-03-28T11:14:13.000Z","rescore_all_solutions":false,"group_id":61,"created_at":"2018-03-21T19:10:33.000Z","updated_at":"2026-03-16T11:15:12.000Z","published_at":"2018-03-21T19:30:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo, I built a function and gave it a name-\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNormie\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFind the nth term of Normie function:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef(n)= 1*f(n-1)+ 2*f(n-3)+ 3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhen n\u0026gt;3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhen n\u0026lt;=3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60271,"title":"Hofstadter G sequence","description":"The Hofstadter G sequence is defined as follows:\r\n\r\nThe first elements of the sequence are 0, 1, 1, 2, 3, 3, 4, 4, 5, 6.\r\nWrite a function to compute  for a given n.\r\nSee https://oeis.org/A005206","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 171.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343.5px 85.85px; transform-origin: 343.5px 85.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.5px; text-align: left; transform-origin: 320.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Hofstadter G sequence is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 49.4px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 24.7px; text-align: left; transform-origin: 320.5px 24.7px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-19px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANwAAABjCAYAAADwxm4hAAAAAXNSR0IArs4c6QAAEd5JREFUeF7tnQkUddUUx/+hJIompYiKEpWQktBkWEVJ8yQyhGhFoRTKUFEkITNlalQqEkohKiqazZEMJUoTMp5f9lmu1xvOfe+8e899b++1Wt/X986995z/vfucPe8F5OQIOAKNIbBAY0/yBzkCjoCc4fwjcAQaRMAZrkGw/VGOgDOcfwOOQIMIOMM1CLY/yhFwhvNvwBFoEIFpMNzOkt4k6WZJT2lwLf4oR6B4BHIy3HKSPiZpM0l3SdpT0keLR8An6Ag0iEAuhltD0pmSHirpGkk7Sfphg+so/VH3l/QiSc+U9HhJS0v6u6QbJH1f0tcNvzsl7S3p55I+V/qiasxvNUmvlfQkW/eikr4t6XBJP61xn84PzcFwMBvgPVDSZZI2MnGy8+BkWACM9kpJb5C0kKRPS/qCpJ9J+nf4O9ghdr9e0v3s33gnjzSmyzCF1m+xq0k6Z4d17yLpFttwjpO0rm3OZ7Q+y4YmMCnDLWk79Ir2gfDx3NjQ3Et/zDqSvijpIZLOkvQSSb8dMOnHGiOuGsb9WtIKpS8ucX6bhA3la5L+YJvI7ZXrHmTfDBvNUyVdmnjPTg+blOE+ZaISICAusYs5SVtL+oydWqdK2i4Ykv4xApgnS7rATsEXzgiIV0tCnDxQ0tv6rOkdQcQ8QNJFYVNi/TNPkzDcWpIuCUDey3bnbWYerbQFsvFwooEL+snjJP0l7dK79bkPSjomcXzJw9aXdL5NcE1JV/SZ7NomIfHTs0yXLXlNE89tEoZDqcc4MjdgJaD9YEmXS1pG0r8kPS18SN9NuC4OeZekoyX9qsY1pQ5l0+CkvkPSYoZH71wXlHSbpPsGMfqTJnaXup4s8xqX4RYOZv8/SlrE/lw2QWTKMuHCb4JBZCubI3+f51MfvW0p24A45QfRlZLQYbFuP6bw9zvx9MZluKq4cLqk5008k+7f4BFmBECUhNBJ0E3mkdiQoxj9TUkbDgEBowpiOC4RrLozTeMy3I6SPm/I4Nx++UyjlLa4d4aPbF8b+iMzFqRdOf1Rm4fT48QMj8HEf1LCfVY21wdDTws+2S2HXHN8ON22t9/xT96UcP/ODhmX4XDiYqGEjghy+D6dRSDfxGEyzPrQUcEXuVe+W098JyQQXBST0g5hIzkh4Sbort+yccdWLNn9LuV3GBnCiIIhbmYpB8MdVtnZZxaoEQtDjESEwrkN4QYYdhIQabGfOX6X77k3lk0MLZyYXaXo4mD+hPvtPmQhVYabeTE8B8PxYbyxq19GpnnjqK5aFgkAwKc2isD/xyGM61E28EgLgapex66PHwunOQEG3zGfFpEqpRL67LU2OaJrhvkVsQEg8kIPk3R9qYvKMS9nuBwo/te6dlXlVnVCszjRGI9jnABwrHuR8F+dZzoO8ZacpDDy9yw4PM/s89+F6BGMIBCi7POHPIKwQCJN2EBwDxBjOrOUg+EODdkB+88sQmkLI0yJdKRIxAjCFKMIf93vpLtryyBGYv2tEiZzGJD41EhY9LDsbVDRk0Y9p43fWRfuInAAj0GEQ3x1O8F7xes25j3VZzrD5YOX7Ijob0KEQpQaRVXj01vD4IMqFxBZz8f6Fklvr/w7vk8CgE+RhBEjhZq2UjInImb2sLkuPmCSnNisBZ32wxbonbKezo5xhsv36sgKIEoEwoL74oRbVx3liFXoZ5EONskBZvlSz72IZkHvg/lSdLmmrZRMt2qpZK5kSPQSJ1sM+VpP0oUJmHV6SA6GO8QCUDsNRIbJs1sTO8iHQ1gXFjdiIwcReg6ZFQ+w8KYleqJ1CH4mnQUxszc8DGfy0y2ErNTsDL6tX4S4UAwopB+9uw8QVAbg9MZw9OgM76D4WzjD5X1F7NhEl3DyYAyBYQbpciRk4sOE+kXrnBN0tI1Nv6kaZBiPM3mLDvitNrXEWlKOVgmukL9W4GajASPiT589L5kmznB5GY67YVkksBvm46RDvMQJjGP81qDbrRR2dCJ1qP2COHiymf35vUox5Ik4Q9JcqoT+huWvC34rRO33m7VyNzvNMTJ91jIE+P0T+V9DmXfMwXDoGogGTv9DAFyfayFNiJgkoXLq/SbodtfZf4ib6HCDklKjSNnPpxdPv4fbvUrHnrISr7PgZAIEiJnEyPQeC24uff7Z5ucMlw3K7DciYfPNVpTpKz13JzuaExSxjIJNTh1BIAfDkbXLh+GUF4EnhlPyYoviqYZ54RzGlI7I6VkaeTGf+t2c4aYO8UQPQK8jZAyjQiRSXc4NkS3bmv430QP84mYRcIZrFu+6T8MAQ+gTFklcAbwv/qSMHgYIp44hkIPh8KMQDeE0HQTwtxEcTjAwwb2cevz/qKJE05mN33UiBJzhJoLPL3YE6iGQg+GwppE+4uQIOAIjEHCG80/EEWgQAWe4BsH2RzkCORiuN63EUXUEHIEBCIzLcKSexPg3Zzj/vByBRATGZbhq7pczXCLYPswRGJfhaL9EWW6IoFSCUJ0cAUdgSlZK0i1ebfcmTSRHzUN/WY7AzCMw7glHUiU1NyC6npJ24uQIOAJTOOHodEojj3uHaPUfhGzlJzjKjoAjkIbAOCdctTQAXT1pM+TkCDgCCQjUZThysSj4QqYxVZgogDrThTsTMPQhjkAyAnUZjswAyilQq4Mo9mpZt+SH+kBHYF4RqMNwJEF+2cpt44f7yLyC5ut2BMZFIJXhKOpJMVJax+IOoKqukyPgCNREIIXhKNv9IaspCLPFRow1H+XDHQFHYBTDxYgSTje6nA4q6eZIOgKOQAICoxjuAElU5UJ3e82A+vAJj/EhjoAjAAKjGI4xLwh9y+jjDXHKpXSFcXQdAUegDwIpDMdldHahGCmFRz07wD8lR2BMBFIZjtvTCBCmI6QL8fJ9Yz7TL3ME5haBOgwHSJxulMSjRBs174e1Y5pbUH3hjsAgBOoyHKFd1EWk59c1oRnFGqHM+T8zw0ujBzqDcqLSBGJpCx+7wRicXtdnWg/pva0oKt1qnMpGgKySl1r7ZBo0LmndhGhNTHchSrefbb5euqHuKYk2VzNFdRmOxeOLIx8OAsBcrYZgNCJYcEUsZMYZussQs0lbJ5ibU5XmfjQz5N+Yf50G9jP18jqyGBhtv5DC9TJL4/p4aLN1lnX9oW0VbZrpNMQmG9/p9Vb0tiNLTJ/mOAxHeg6N3he0VkOxr3X6U+85ch1LYqWtEy+DLIRBPj/6pcGIq9oOuMIkD/Zrp4oAGzJRSWygdECl6Uu1KWP14VtKokUXhjn+3HWqM2vp5uMwHFONLW/5O61iySAYl7Y2gDm1Tg3NB7dLKONNI8IL7BQkEsapLAT4rg6VtK9Na59Kt9dhM2U8nYIoUkUjy5mjcRmOGiboT9Ak4KCncaLRH5v2s5yWNOxLIQw27J7HpAz2MY0iELNKeCidTvHlptCi1opr5SBi/jLlgq6NGZfhqnocYgLRKHWJ3s6XW2N40n0IkO5tHj/snhQxOtraOdV9to+fHgIbmfGDTRSDCCrAzTUed0IwyG1fY3ynho7LcCi48chHBKCbS11CD9vKLuLv29S9wQyORy9eLeiza0m6UNJPbI3oNUgDWPew0F5Z6NoXNiPX8jY/LI0fKHSurUwrB8Nx0mCFqkO4Fehxxi4IdaE5fJ311R3LZoOITtdTDAyc+BiQbjRsyNBY0W5KPZnlCm01jKHjWJvnn8zSeGddMGZ5fFsMx6kYFWr8euzqpdDmoXTEiRkmw8d3Uo37cLphCILpEK3XNzEb4wMnBcapmBqFf5Km9KURp/K6Nil8abh5nCoItMVwMBlmfeioIOPvVdBboW92jjqbO4SNBH2kDl0UREZcJEgMp5llDysuhqQNJJ1nN8M1c2udGzcwdlnT2eKjUBewOju1zHCIkXxAiE4QboBhJwGWKz5Ads6oG8QlYNnkNKg2ne/qC8YJfJPFqlLz87DgbtkxnBJE2ECvMn0IFwynXWnEiXx+ZVIYxfDXDqLVzcJNYDzvuErUPSUHs46EUBoefefTxgmHo5pG8ZGIHkGUGkXMlY8NwwF0pCRK9s0KUcH6FNNtvxrqfZ4uiT8j4QzepaZEsG2GdCoiRDDtj6Kq/nZX8MMRBphCRKJUQ7hmupJ3GwxHab2rKm+iTmgWJxrjCZ7GcDBsB0152SWNwcWBznOJxYz26j9E3mBIeY5ZKlPmjnn9+JSBQ8ZgkY6GkGG32qNS66ZOaBZSC+Mh3ESjIpcwuJGtEr8DGBv9l1ORDZkTk02iSGqD4RCdqn4ZREXAGkXLmI7AnKNRYdQ1XfodFwCnN2LlKj0Y4cvCFfC3cMItYYHbpa2tqvtimcSVQWzkKOIUjkaqQ0KgOlUG+hEuh/dazCW+X9LDYk1UfiN0DLEbUTwa5EY9u/Hf22A4FomFLe5khGalZJFXfX/TTIJtw0pJYd0YWcEHx4dXJYxKiNDnBD3pGY1/JWkPJPofN0Z09bCm6xIuJVIohufhNI+GoeqlbNLkYq4taVNzrPe7NVZS0sfIPCiS2mK4an85HOiEh42iqqMcsWFaRWjbsFISrE0U/SBR+QyLqGfnZgcvlbDKYgSDUjZSmPP3loLFqbj4AP8i1k6Cm0fp7ZxwfE/F+v7aYjiAxqK1njl5cXwPS2YlsJndEzHlNhOr+DgjIcPTpw7/FM1FMKHzO3oRf+fEOKLUr9T0LPQtdmYK7lYJay7ObtbO2migwgaFBQ8sSiJcA+RJciKhc2JNHTZHwvnIhYM4wTbrsxiCAlgrojYi9y0lLbjuXNpiOOaJWRi/0yIWuIwFbpAuV20ggvWOU6iXUJ7Rc/5sYgdyPjI/HzHMitm6ROIdML+lrEhTLNgU5xr9b/jdOAEwmrBBDdJ12l5jtR01TESKzqBUK/yd8V0SacP76iUYEsZEVCQoutPUJsMB3Jph1yJbG+YjnAlxAIBxjPOBrWS+qJ1NAT85/Hmg/d6P4TDGHG6nwf5mZMCPBZOWarniVL7U1oeJvPfjjO4CxCSyI3CrgEfuTPucHzKGEKQLNhE2QOIp0dt5r/cxoxCWRiSc263QMBE1vUHOGENYN98pvsmLeybJqU9gAOMiYUhB/eC5xVHbDAcgzIGMX2R0XgCmb049mjyidPMf4iYgDitEu7EZFchAJ3sBIwQMS8zmOFEfTb0sMtjRy2A6wrp6iY+K/ENiKTEukRGPn6t04h0itSAiIwpTKoN3zfvED8t/55qDG6brR4T8XW0/DIquQZ3Af8k3hK+SjRVrbhvEaU2zm9is9B5zKIHhcgETEx5Jdoyiye62exL1gB7k1C0E2HzjJsspNoiRvmG1UsiyuKyFJRK8geOf7405YnPoS7PEcIgbOFE51WISK8o2IlgMqG3hXfgjJ0QApzjvlZo2/dKSCAvDoBKzKCZ83FiXw2B8c3yD+ExnnuFwBhN1gvMzOj2xhPJv6D0Hm0iGDuHULQReYVIKeiBZE70Uo2nw5+3W8tIQkTFozTzDxWiFatRKNEagv6ELwIyDdIWW35M/fggCSGHorjuFMQeZvhtFS/RCEnLRETGe5MjymORlzA3D0RwShRWZP4YT8TKuCA7Ya80ZO3M1Dif5Mjp47SZWopEIFhiO8g0YlAjzw1BWfb9t+WXnhuE6+P34lKeMQBt+WWe4Kb9Uv325CMBwTftlneHK/R58ZlNGoI5fNvZBTJkSwRfYDPqRM1wKgj5mJhGo45cl5hNzfgoRkEFWQqMMh+XvOHsieUmE6Tg5AiUh0IZfdmonXLV+Be2ICatxcgRKQaAtv+zUGA7HHnUHCbfBuUxaBsHHTo5ACQi04ZfFX4hrAl4g7vOOfkCMG9rFvaiVEUtSo6DC3U6OQAkINO2XJbqEQG0SYCGyXggrJD3p/2gShiMiOuavUdKM0gROjoAjMASBSRiO28bSbfydWhN0wnFyBByBAQhMynAop4RPUbKO2hQUecFs6uQIOAJ9EJiU4bgl1bfI0l7M6k2iz1EywMkRcAR6EMjBcNySKH1q4VM7kmDhLQpuqeQfgSPQGgK5GI4FUI8DnW5D6+NMLcXegjitLdQf7AiUgEBOhovrwTxKXQeKuHimdQlv2edQDALTYLhiFucTcQRKQ8AZrrQ34vOZaQT+A9RlapEaIyLRAAAAAElFTkSuQmCC\" width=\"110\" height=\"49.5\" style=\"width: 110px; height: 49.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.9px; text-align: left; transform-origin: 320.5px 10.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first elements of the sequence are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e0, 1, 1, 2, 3, 3, 4, 4, 5, 6\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 11.25px; text-align: left; transform-origin: 320.5px 11.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003efor a given\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.5px; text-align: left; transform-origin: 320.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSee \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A005206\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://oeis.org/A005206\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function G = G_sequence(n)\r\n\r\nend","test_suite":"all_glo = [0, 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 30, 31, 32, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 43, 44, 45, 45, 46, 46, 47, 48, 48, 49, 50, 50, 51, 51, 52, 53, 53, 54, 55, 55, 56, 56, 57, 58, 58, 59, 59, 60, 61, 61, 62, 63, 63, 64, 64, 65, 66, 66, 67, 67, 68, 69, 69, 70, 71, 71, 72, 72, 73, 74, 74, 75, 76, 76, 77, 77, 78, 79, 79, 80, 80, 81, 82, 82, 83, 84, 84, 85, 85, 86, 87, 87, 88, 88, 89, 90, 90, 91, 92, 92, 93, 93, 94, 95, 95, 96, 97, 97, 98, 98, 99, 100, 100, 101, 101, 102, 103, 103, 104, 105, 105, 106, 106, 107, 108, 108, 109, 110, 110, 111, 111, 112, 113, 113, 114, 114, 115, 116, 116, 117, 118, 118, 119, 119, 120, 121, 121, 122, 122, 123, 124, 124, 125, 126, 126, 127, 127, 128, 129, 129, 130, 131, 131, 132, 132, 133, 134, 134, 135, 135, 136, 137, 137, 138, 139, 139, 140, 140, 141, 142, 142];\r\nn = randi([90,numel(all_glo)]) \r\ny_correct = all_glo(n+1)\r\n\r\n%%\r\n% Only for this random test, n and y_correct are displayed but their definition is hidden.\r\nn\r\ny_obtained = G_sequence(n)\r\ny_correct\r\nassert(isequal(y_obtained,y_correct));\r\n\r\n\r\n%%\r\nn = 76\r\ny_obtained = G_sequence(n)\r\ny_correct = 47\r\nassert(isequal(y_obtained,y_correct));\r\n\r\n%%\r\nyy_correct = [0, 1, 1, 2, 3, 3, 4, 4, 5, 6];\r\nfor n = 0:numel(yy_correct)-1\r\n    y_obtained = G_sequence(n);\r\n    y_correct = yy_correct(n+1);\r\n    assert(isequal(y_obtained,y_correct));\r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-11T17:00:10.000Z","updated_at":"2026-03-02T09:18:08.000Z","published_at":"2024-05-11T17:00:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Hofstadter G sequence is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$$\\\\begin{cases}\\nG_0 = 0\\\\\\\\\\nG_n = n-G_{G_{n-1}}\\n\\\\end{cases}$$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first elements of the sequence are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0, 1, 1, 2, 3, 3, 4, 4, 5, 6\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eG_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003efor a given\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A005206\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://oeis.org/A005206\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42835,"title":"Return the sequence element II","description":"Given positive integers x and n, return a positive integer, y, which is the nth term in the \u003chttps://en.wikipedia.org/wiki/Juggler_sequence Juggler sequence\u003e beginning with x.\r\n\r\nThe Juggler sequence is defined by:\r\n\r\na(i+1) = floor(a(i)^0.5) , for even a(i).\r\n\r\na(i+1) = floor(a(i)^1.5) , for odd a(i).\r\n\r\nFor the purpose of this problem, the first element in the sequence is a(1) = x.\r\n\r\nExample:\r\n\r\nx = 3\r\n\r\nn = 5\r\n\r\ny = 6","description_html":"\u003cp\u003eGiven positive integers x and n, return a positive integer, y, which is the nth term in the \u003ca href = \"https://en.wikipedia.org/wiki/Juggler_sequence\"\u003eJuggler sequence\u003c/a\u003e beginning with x.\u003c/p\u003e\u003cp\u003eThe Juggler sequence is defined by:\u003c/p\u003e\u003cp\u003ea(i+1) = floor(a(i)^0.5) , for even a(i).\u003c/p\u003e\u003cp\u003ea(i+1) = floor(a(i)^1.5) , for odd a(i).\u003c/p\u003e\u003cp\u003eFor the purpose of this problem, the first element in the sequence is a(1) = x.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003ex = 3\u003c/p\u003e\u003cp\u003en = 5\u003c/p\u003e\u003cp\u003ey = 6\u003c/p\u003e","function_template":"function y = juggler(x,n)\r\n  y = x + n;\r\nend","test_suite":"%%\r\nx = 3;\r\nn = 5;\r\ny_correct = 6;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 33;\r\nn = 3;\r\ny_correct = 2598;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 45;\r\nn = 4;\r\ny_correct = 72;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 163;\r\nn = 23;\r\ny_correct = 333;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 37;\r\nn = 13;\r\ny_correct = 34276462;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 37;\r\nn = 18;\r\ny_correct = 1;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 37;\r\nn = 99;\r\ny_correct = 1;\r\nassert(isequal(juggler(x,n),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":45,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-27T19:07:54.000Z","updated_at":"2026-03-05T12:02:09.000Z","published_at":"2016-04-27T19:07:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven positive integers x and n, return a positive integer, y, which is the nth term in the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Juggler_sequence\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eJuggler sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e beginning with x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Juggler sequence is defined by:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(i+1) = floor(a(i)^0.5) , for even a(i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(i+1) = floor(a(i)^1.5) , for odd a(i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor the purpose of this problem, the first element in the sequence is a(1) = x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45224,"title":"Wythoff Sequence","description":"\r\nFind the lower Wythoff sequence up to n.\r\n\r\nFor more information, \u003chttps://oeis.org/A000201\u003e","description_html":"\u003cp\u003eFind the lower Wythoff sequence up to n.\u003c/p\u003e\u003cp\u003eFor more information, \u003ca href = \"https://oeis.org/A000201\"\u003ehttps://oeis.org/A000201\u003c/a\u003e\u003c/p\u003e","function_template":"function y=wythoff(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = 1;\r\nassert(isequal(wythoff(n),y_correct))\r\n%%\r\nn = 10;\r\ny_correct = [1,3,4,6,8,9,11,12,14,16];\r\nassert(isequal(wythoff(n),y_correct))\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2019-12-04T12:02:31.000Z","updated_at":"2026-03-16T11:21:35.000Z","published_at":"2019-12-04T12:20:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the lower Wythoff sequence up to n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor more information,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A000201\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://oeis.org/A000201\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":3011,"title":"Self-similarity 2 - Every third term","description":"Self-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003chttps://oeis.org/selfsimilar.html OEIS page\u003e for more information.\r\n\r\nIn this problem, you are to check if the sequence is self-similar by every third term. The problem set assumes that you start with the first element and then take every third element thereafter of the original sequence, and compare that result to the first third of the original sequence. The function should return true if the extracted sequence is equal to the first third of the original sequence.\r\n\r\nFor example,\r\n\r\n* seq_original_set = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4]\r\n* seq_every_third = [0, , , 1, , , 2, , , 1, , , 2, , ,] (extra commas are instructional and should not be in the every-other series) \r\n* seq_orig_first_third = [0, 1, 2, 1, 2]\r\n\r\nSince seq_every_third = seq_orig_first_third, the set is self-similar.\r\n\r\nThis problem is related to \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term Problem 3010\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms Problem 3012\u003e.","description_html":"\u003cp\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003ca href = \"https://oeis.org/selfsimilar.html\"\u003eOEIS page\u003c/a\u003e for more information.\u003c/p\u003e\u003cp\u003eIn this problem, you are to check if the sequence is self-similar by every third term. The problem set assumes that you start with the first element and then take every third element thereafter of the original sequence, and compare that result to the first third of the original sequence. The function should return true if the extracted sequence is equal to the first third of the original sequence.\u003c/p\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cul\u003e\u003cli\u003eseq_original_set = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4]\u003c/li\u003e\u003cli\u003eseq_every_third = [0, , , 1, , , 2, , , 1, , , 2, , ,] (extra commas are instructional and should not be in the every-other series)\u003c/li\u003e\u003cli\u003eseq_orig_first_third = [0, 1, 2, 1, 2]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eSince seq_every_third = seq_orig_first_third, the set is self-similar.\u003c/p\u003e\u003cp\u003eThis problem is related to \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term\"\u003eProblem 3010\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms\"\u003eProblem 3012\u003c/a\u003e.\u003c/p\u003e","function_template":"function [tf] = self_similarity_2(seq)\r\n\r\ntf = 0;\r\n\r\nend\r\n","test_suite":"%%\r\nseq = [1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 2, 0, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 3, 3, 0, 0, 2, 1, 4, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 4, 0, 1, 2, 0, 3, 0, 4, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 3, 2, 3, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 4, 7, 2, 5, 9, 1, 10, 19, 4, 13, 22, 7, 16, 25, 2, 11, 20, 5, 14, 23, 8, 17, 26, 1, 28, 55, 10, 37, 64, 19, 46, 73, 4, 31, 58, 13, 40, 67, 22, 49, 76, 7, 34, 61, 16, 43, 70, 25, 52, 79, 2, 29, 56, 11, 38, 65, 20, 47, 74, 5, 32, 59, 14, 41, 68, 23, 50, 77, 8, 35, 62, 17, 44, 71];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 3, 2, 2, 3, 1, 1, 2, 1, 1, 3, 2, 2, 3, 0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3, 4, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 11, 12, 2, 12, 22, 1, 11, 12, 11, 12, 112, 12, 112, 122, 2, 12, 22, 12, 112, 122, 22, 122, 222, 1, 11, 12, 11, 111, 112, 12, 112, 122, 11, 111, 112, 111, 1111, 1112, 112, 1112, 1122, 12, 112, 122, 112, 1112, 1122, 122, 1122, 1222, 2, 12, 22, 12, 112];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 4, 1, 2, 5, 4, 5, 8, 1, 2, 5, 1, 3, 6, 5, 6, 9, 4, 5, 8, 5, 6, 9, 8, 9, 12, 1, 2, 5, 2, 3, 6, 5, 6, 9, 2, 3, 6, 3, 4, 7, 6, 7, 10, 5, 6, 9, 6, 7, 10, 9, 10, 13, 4, 5, 8, 5, 6, 9, 8, 9, 12, 5, 6, 9, 6, 7];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 12, 36, 12, 84, 72, 36, 96, 180, 12, 216, 180, 84, 168, 288, 72, 372, 216, 36, 240, 504, 96, 432, 288, 180, 372, 504, 12, 672, 360, 216, 384, 756, 144, 648, 576, 84, 456, 720, 168, 1080, 504, 288, 528, 1008, 72, 864, 576, 372, 684, 1116, 216, 1176, 648, 36];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 2, 0, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 3, 3, 0, 0, 2, 1, 4, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 4, 0, 1, 2, 0, 3, 0, 4, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 3, 2, 3, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 1, 0, 1, 2, 1, 1, 2, 0, 0, 1, 0, 0, 3, 2, 2, 3, 1, 1, 2, 1, 1, 3, 2, 2, 3, 0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3, 4, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 4, 6, 3, 6, 9, 2, 4, 6, 4, 8, 12, 6, 12, 18, 3, 6, 9, 6, 12, 18, 9, 18, 27, 2, 4, 6, 4, 8, 12, 6, 12, 18, 4, 8, 12, 8, 16, 24, 12, 24, 36, 6, 12, 18, 12, 24, 36, 18, 36, 54, 3, 6, 9, 6, 12, 18, 9, 18, 27, 6, 12, 18, 12, 24, 36, 18, 36, 54, 9, 18, 27, 18, 36, 54, 27, 54];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 4, 1, 2, 5, 4, 5, 8, 1, 2, 5, 2, 3, 6, 5, 6, 9, 4, 5, 8, 5, 6, 9, 8, 9, 12, 1, 2, 5, 2, 3, 6, 5, 6, 9, 2, 3, 6, 3, 4, 7, 6, 7, 10, 5, 6, 9, 6, 7, 10, 9, 10, 13, 4, 5, 8, 5, 6, 9, 8, 9, 12, 5, 6, 9, 6, 7];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 12, 36, 12, 84, 72, 36, 96, 180, 12, 216, 144, 84, 168, 288, 72, 372, 216, 36, 240, 504, 96, 432, 288, 180, 372, 504, 12, 672, 360, 216, 384, 756, 144, 648, 576, 84, 456, 720, 168, 1080, 504, 288, 528, 1008, 72, 864, 576, 372, 684, 1116, 216, 1176, 648, 36];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 2, 1, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 0, 1, 2, 1, 2, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 3, 1, 3, 1, 2, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2, 2, 3, 1, 3, 1, 2, 1, 2, 3, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 4, 7, 2, 5, 8, 1, 10, 19, 4, 13, 22, 7, 16, 25, 2, 11, 20, 5, 14, 23, 8, 17, 26, 1, 28, 55, 10, 37, 64, 19, 46, 73, 4, 31, 58, 13, 40, 67, 22, 49, 76, 7, 34, 61, 16, 43, 70, 25, 52, 79, 2, 29, 56, 11, 38, 65, 20, 47, 74, 5, 32, 59, 14, 41, 68, 23, 50, 77, 8, 35, 62, 17, 44, 71];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 2, 1, 2, 3, 2, 3, 4, 1, 3, 5, 2, 4, 6, 3, 5, 7, 2, 4, 6, 3, 5, 7, 4, 6, 8, 1, 2, 3, 3, 4, 5, 5, 6, 7, 2, 3, 4, 4, 5, 6, 6, 7, 8, 3, 4, 5, 5, 6, 7, 7, 8, 9, 2, 3, 4, 4, 5, 6, 6, 7, 8, 3, 4, 5, 5, 6, 7, 7, 8, 9, 4, 5, 6, 6, 7, 8, 8, 9, 10, 1, 3, 5, 2, 4, 6, 3, 5, 7, 3, 5, 7, 4, 6, 8, 5, 7, 9, 5, 7, 9];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 1, 1, 3, 1, 1, 2, 3, 2, 1, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [\t1, 2, 0, 2, 6, 0, 0, 4, 0, 2, 0, 0, 6, 4, 0, 0, 6, 0, 0, 4, 0, 4, 0, 0, 0, 2, 0, 2, 12, 0, 0, 4, 0, 0, 0, 0, 6, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 6, 6, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 6, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 12, 0, 0, 4, 0, 2, 0, 0, 12, 0, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 0, 6, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 3, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 6, 0, 0, 6, 4, 2, 4, 12, 6, 4, 8, 0, 10, 0, 0, 16, 8, 6, 4, 12, 4, 14, 8, 2, 34, 12, 4, 16, 40, 12, 12, 48, 6, 28, 8, 4, 44, 24, 8, 16, 44, 0, 12, 24, 10, 58, 16, 0, 28, 36, 0, 24, 100, 16, 16, 48, 8, 28, 16, 6, 62];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 6, 0, 0, 4, 0, 2, 0, 0, 6, 6, 4, 0, 10, 12, 0, 4, 8, 4, 4, 0, 0, 14, 8, 2, 12, 12, 0, 4, 8, 0, 8, 0, 6, 4, 4, 6, 8, 24, 4, 16, 8, 0, 8, 0, 10, 18, 8, 12, 34, 12, 0, 24, 44, 4, 8, 24, 8, 28, 12, 4, 46, 48, 4, 28, 36, 0, 16];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 4, 5, 2, 5, 8, 1, 3, 5, 4, 13, 14, 5, 14, 17, 2, 5, 8, 5, 14, 17, 8, 17, 26, 1, 4, 5, 4, 13, 14, 5, 14, 17, 4, 13, 14, 13, 40, 41, 14, 41, 44, 5, 14, 17, 14, 41, 44, 17, 44, 53, 2, 5, 8, 5, 14, 17, 8, 17, 26, 5, 14, 17, 14, 41, 44, 17, 44, 53, 8, 17, 26, 17, 44, 53, 26, 53, 80];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 4, 20, 24, 4, 32, 52, 4, 24, 48, 20, 56, 32, 24, 116, 72, 4, 80, 120, 32, 48, 96, 52, 124, 56, 4, 160, 120, 24, 128, 244, 48, 72, 192, 20, 152, 80, 56, 312, 168, 32, 176, 240, 24, 96, 192, 116, 228, 124, 72, 280, 216, 4, 288, 416, 80, 120, 240, 120, 248, 128, 32, 500];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 4, 6, 3, 6, 9, 2, 4, 6, 4, 8, 16, 6, 12, 18, 3, 6, 9, 6, 12, 18, 9, 18, 27, 2, 4, 6, 4, 8, 12, 6, 12, 18, 4, 8, 12, 8, 16, 24, 12, 24, 36, 6, 12, 18, 12, 24, 36, 18, 36, 54, 3, 6, 9, 6, 12, 18, 9, 18, 27, 6, 12, 18, 12, 24, 36, 18, 36, 54, 9, 18, 27, 18, 36, 54, 27, 54];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 4, 5, 2, 5, 8, 1, 4, 5, 4, 13, 14, 5, 14, 17, 2, 5, 8, 5, 14, 17, 8, 17, 26, 1, 4, 5, 4, 13, 14, 5, 14, 17, 4, 13, 14, 13, 40, 41, 14, 41, 44, 5, 14, 17, 14, 41, 44, 17, 44, 53, 2, 5, 8, 5, 14, 17, 8, 17, 26, 5, 14, 17, 14, 41, 44, 17, 44, 53, 8, 17, 26, 17, 44, 53, 26, 53, 80];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 6, 0, 0, 4, 0, 2, 0, 0, 6, 8, 4, 2, 10, 12, 0, 4, 8, 4, 4, 0, 0, 14, 8, 2, 12, 12, 0, 4, 8, 0, 8, 0, 6, 4, 4, 6, 8, 24, 4, 16, 8, 0, 8, 0, 10, 18, 8, 12, 34, 12, 0, 24, 44, 4, 8, 24, 8, 28, 12, 4, 46, 48, 4, 28, 36, 0, 16];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 4, 20, 24, 4, 32, 52, 4, 24, 48, 40, 56, 32, 64, 116, 72, 4, 80, 120, 32, 48, 96, 52, 124, 56, 4, 160, 120, 24, 128, 244, 48, 72, 192, 20, 152, 80, 56, 312, 168, 32, 176, 240, 24, 96, 192, 116, 228, 124, 72, 280, 216, 4, 288, 416, 80, 120, 240, 120, 248, 128, 32, 500];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 11, 12, 2, 12, 22, 1, 11, 12, 11, 111, 112, 12, 112, 122, 2, 12, 22, 12, 112, 122, 22, 122, 222, 1, 11, 12, 11, 111, 112, 12, 112, 122, 11, 111, 112, 111, 1111, 1112, 112, 1112, 1122, 12, 112, 122, 112, 1112, 1122, 122, 1122, 1222, 2, 12, 22, 12, 112];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 4, 4, 12, 4, 4, 4, 4, 12, 4, 4, 12, 4, 12, 4, 12, 4, 4, 12, 4, 4, 4, 4, 20, 12, 4, 4, 12, 12, 4, 4, 4, 12, 12, 4, 12, 4, 12, 12, 12, 4, 4, 4, 12, 4, 4, 4, 4, 20, 12, 12, 12, 4, 12, 4, 4, 12, 4, 12, 12, 4, 4, 4, 36, 4, 4, 12, 4, 12, 4, 4, 12, 12, 20, 4, 4, 12, 4, 12, 4, 12, 4, 4, 36];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 4, 3, 4, 3, 1, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 3, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 2, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2, 2, 3, 1, 3, 1, 2, 1, 2, 3, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 2, 1, 2, 3, 2, 3, 4, 1, 2, 5, 2, 4, 5, 3, 5, 7, 2, 4, 6, 3, 5, 7, 4, 6, 8, 1, 2, 3, 3, 4, 5, 5, 6, 7, 2, 3, 4, 4, 5, 6, 6, 7, 8, 3, 4, 5, 5, 6, 7, 7, 8, 9, 2, 3, 4, 4, 5, 6, 6, 7, 8, 3, 4, 5, 5, 6, 7, 7, 8, 9, 4, 5, 6, 6, 7, 8, 8, 9, 10, 1, 3, 5, 2, 4, 6, 3, 5, 7, 3, 5, 7, 4, 6, 8, 5, 7, 9, 5, 7, 9];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 4, 4, 12, 4, 4, 8, 4, 12, 4, 4, 12, 4, 12, 4, 12, 4, 4, 12, 4, 4, 4, 4, 20, 12, 4, 4, 12, 12, 4, 4, 4, 12, 12, 4, 12, 4, 12, 12, 12, 4, 4, 4, 12, 4, 4, 4, 4, 20, 12, 12, 12, 4, 12, 4, 4, 12, 4, 12, 12, 4, 4, 4, 36, 4, 4, 12, 4, 12, 4, 4, 12, 12, 20, 4, 4, 12, 4, 12, 4, 12, 4, 4, 36];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [\t1, 2, 0, 2, 6, 0, 1, 4, 0, 2, 0, 0, 6, 4, 1, 0, 6, 0, 0, 4, 0, 4, 0, 0, 0, 2, 0, 2, 12, 0, 0, 4, 0, 0, 0, 0, 6, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 6, 6, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 6, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 12, 0, 0, 4, 0, 2, 0, 0, 12, 0, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 0, 6, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 6, 0, 2, 6, 4, 2, 4, 12, 6, 4, 8, 2, 10, 0, 0, 16, 8, 6, 4, 12, 4, 14, 8, 2, 34, 12, 4, 16, 40, 12, 12, 48, 6, 28, 8, 4, 44, 24, 8, 16, 44, 0, 12, 24, 10, 58, 16, 0, 28, 36, 0, 24, 100, 16, 16, 48, 8, 28, 16, 6, 62];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 2, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 0, 1, 2, 1, 2, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":66,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":30,"created_at":"2015-02-13T04:22:00.000Z","updated_at":"2026-03-11T15:38:45.000Z","published_at":"2015-02-13T04:22:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/selfsimilar.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOEIS page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more information.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, you are to check if the sequence is self-similar by every third term. The problem set assumes that you start with the first element and then take every third element thereafter of the original sequence, and compare that result to the first third of the original sequence. The function should return true if the extracted sequence is equal to the first third of the original sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_original_set = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_every_third = [0, , , 1, , , 2, , , 1, , , 2, , ,] (extra commas are instructional and should not be in the every-other series)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_orig_first_third = [0, 1, 2, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince seq_every_third = seq_orig_first_third, the set is self-similar.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is related to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3010\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3012\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":59791,"title":"Complete a geometric sequence","description":"In Cody Problem 59786 minnolina asks us to find the integer that completes a randomly sorted arithmetic sequence with one missing element. This problem is similar, but it deals with geometric sequences. For example, in the list [4 8 32 128 16 2], the common ratio is 2, and the missing element is 64. \r\nWrite a function to find the missing element in a randomly sorted geometric sequence. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59786\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 59786\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 299.9px 8px; transform-origin: 299.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e minnolina asks us to find the integer that completes a randomly sorted arithmetic sequence with one missing element. This problem is similar, but it deals with geometric sequences. For example, in the list \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46.2px 8px; transform-origin: 46.2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[4 8 32 128 16 2]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 171.133px 8px; transform-origin: 171.133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the common ratio is 2, and the missing element is 64. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 267.875px 8px; transform-origin: 267.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find the missing element in a randomly sorted geometric sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = completeGeomSeq(x)\r\n   y = mean(x);\r\nend","test_suite":"%%\r\nx = [4 8 32 128 16 2];\r\ny = completeGeomSeq(x);\r\ny_correct = 64;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nx = [19683 2187 9 3 243 27 81 6561];\r\ny = completeGeomSeq(x);\r\ny_correct = 729;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nx = [256 67108864 262144 1048576 16384 64 65536 1024 4096 1073741824 16777216 4194304];\r\ny = completeGeomSeq(x);\r\ny_correct = 268435456;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nx = [390625 125 78125 15625 625 3125 9765625];\r\ny = completeGeomSeq(x);\r\ny_correct = 1953125;\r\nassert(isequal(y,y_correct))\r\n\r\n%% \r\nfor k = 1:randi(8)\r\n    b = 1+randi(12);\r\n    e1 = randi(4);\r\n    en = e1+2+randi(6);\r\n    x1 = b.^(e1:en);\r\n    indx = 1+randi(length(x1)-2);\r\n    y_correct = x1(indx);\r\n    x1(indx) = [];\r\n    x = x1(randperm(length(x1)));\r\n    y = completeGeomSeq(x);\r\n    assert(isequal(y,y_correct))\r\nend","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-03-31T23:55:34.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-31T23:55:30.000Z","updated_at":"2026-03-02T14:55:52.000Z","published_at":"2024-03-31T23:55:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59786\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 59786\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e minnolina asks us to find the integer that completes a randomly sorted arithmetic sequence with one missing element. This problem is similar, but it deals with geometric sequences. For example, in the list \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[4 8 32 128 16 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the common ratio is 2, and the missing element is 64. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find the missing element in a randomly sorted geometric sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47265,"title":"Find Logic 10","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 191.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 95.8333px; transform-origin: 174px 95.8333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 120\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 60\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 20\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 120;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 60;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx=5;\r\ny_correct = 1;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":415,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-04T08:47:44.000Z","updated_at":"2026-02-14T07:05:44.000Z","published_at":"2020-11-04T08:47:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 60\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 20\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57869,"title":"Identify de Polignac numbers","description":"The numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, , and . The numbers 127 and 331, which are examples of de Polignac numbers, cannot be written in this way.\r\nWrite a function that determines whether an odd number is a de Polignac number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 297.55px 8px; transform-origin: 297.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"125 = 109+2^4\" style=\"width: 96px; height: 19px;\" width=\"96\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"329 = 73+2^8\" style=\"width: 88.5px; height: 19px;\" width=\"88.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 320.392px 8px; transform-origin: 320.392px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The numbers 127 and 331, which are examples of de Polignac numbers, cannot be written in this way.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 255.042px 8px; transform-origin: 255.042px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that determines whether an odd number is a de Polignac number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isdePolignac(n)\r\n  tf = isequal(n,p+2^k);\r\nend","test_suite":"%%\r\nassert(isdePolignac(1))\r\n\r\n%%\r\nassert(~isdePolignac(17))\r\n\r\n%%\r\nassert(~isdePolignac(75))\r\n\r\n%%\r\nassert(isdePolignac(127))\r\n\r\n%%\r\nassert(isdePolignac(331))\r\n\r\n%%\r\nassert(~isdePolignac(531))\r\n\r\n%%\r\nassert(isdePolignac(905))\r\n\r\n%%\r\nassert(isdePolignac(1619))\r\n\r\n%%\r\nassert(~isdePolignac(2261))\r\n\r\n%%\r\nassert(isdePolignac(7535))\r\n\r\n%%\r\nassert(~isdePolignac(10413))\r\n\r\n%%\r\nassert(isdePolignac(21453))\r\n\r\n%%\r\nassert(isdePolignac(45233))\r\n\r\n%%\r\nassert(~isdePolignac(70999))\r\n\r\n%%\r\nassert(~isdePolignac(96415))\r\n\r\n%%\r\nassert(~isdePolignac(121399))\r\n\r\n%%\r\nassert(isdePolignac(148243))\r\n\r\n%%\r\nassert(isdePolignac(172841))\r\n\r\n%%\r\nassert(isdePolignac(201599))\r\n\r\n%%\r\nassert(isdePolignac(227107))\r\n\r\n%%\r\nassert(isdePolignac(253151))\r\n\r\n%%\r\nassert(~isdePolignac(267267))\r\n\r\n%%\r\nassert(~isdePolignac(271271))\r\n\r\n%%\r\nassert(isdePolignac(273421))\r\n\r\n%%\r\nassert(isdePolignac(542459))\r\n\r\n%%\r\nassert(isdePolignac(2000039))\r\n\r\n%%\r\nassert(~isdePolignac(123456789))\r\n\r\n%%\r\nassert(isdePolignac(123456791))\r\n\r\n%%\r\nassert(isequal(bin2dec(num2str(arrayfun(@isdePolignac,5893:2:5933)')'),288))\r\n\r\n%%\r\nassert(isequal(bin2dec(num2str(arrayfun(@isdePolignac,21671:10:21791)')'),4624))\r\n\r\n%%\r\nfiletext = fileread('isdePolignac.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-29T05:27:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-29T05:27:08.000Z","updated_at":"2025-12-25T08:44:06.000Z","published_at":"2023-03-29T05:27:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"125 = 109+2^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e125 = 109+2^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"329 = 73+2^8\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e329 = 73+2^8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The numbers 127 and 331, which are examples of de Polignac numbers, cannot be written in this way.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that determines whether an odd number is a de Polignac number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47239,"title":"Find Logic 5","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 191.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 95.8333px; transform-origin: 174px 95.8333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the logic\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 14\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which returns 'x' th term of logic\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 2;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 20;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 44;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":67,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-03T16:42:59.000Z","updated_at":"2026-03-16T11:57:14.000Z","published_at":"2020-11-03T16:42:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the logic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which returns 'x' th term of logic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60276,"title":"Hofstadter H sequence","description":"The Hofstadter H sequence is defined as follows:\r\n\r\nThe first elements of the sequence are 0, 1, 1, 2, 3, 4, 4, 5, 5, 6.\r\nWrite a function to compute  for a given n.\r\nSee https://oeis.org/A005374","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 175.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 87.75px; transform-origin: 407px 87.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Hofstadter H sequence is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 54px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 27px; text-align: left; transform-origin: 384px 27px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-21px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"118\" height=\"54\" style=\"width: 118px; height: 54px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first elements of the sequence are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e0, 1, 1, 2, 3, 4, 4, 5, 5, 6\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003efor a given\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSee \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A005374\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://oeis.org/A005374\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function h = H_sequence(n)\r\n\r\nend","test_suite":"all_glo = [0, 1, 1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 13, 13, 14, 14, 15, 16, 17, 17, 18, 18, 19, 20, 20, 21, 22, 23, 23, 24, 24, 25, 26, 26, 27, 28, 29, 29, 30, 31, 32, 32, 33, 33, 34, 35, 35, 36, 37, 38, 38, 39, 40, 41, 41, 42, 42, 43, 44, 45, 45, 46, 46, 47, 48, 48, 49, 50, 51, 51, 52, 53, 54, 54, 55, 55, 56, 57, 58, 58, 59, 59, 60, 61, 61, 62, 63, 64, 64, 65, 65, 66, 67, 67, 68, 69, 70, 70, 71, 72, 73, 73, 74, 74, 75, 76, 77, 77, 78, 78, 79, 80, 80, 81, 82, 83, 83, 84, 84, 85, 86, 86, 87, 88, 89, 89, 90, 91, 92, 92, 93, 93, 94, 95, 95, 96, 97, 98, 98, 99, 100, 101, 101, 102, 102, 103, 104, 105, 105, 106, 106, 107, 108, 108, 109, 110, 111, 111, 112, 112, 113, 114, 114, 115, 116, 117, 117, 118, 119, 120, 120, 121, 121, 122, 123, 123, 124, 125, 126, 126, 127, 128, 129, 129, 130, 130, 131, 132, 133, 133, 134, 134, 135, 136, 136, 137, 138, 139, 139, 140, 141, 142, 142, 143, 143, 144, 145, 146, 146, 147, 147, 148, 149, 149, 150, 151, 152, 152, 153, 153, 154, 155, 155, 156, 157];\r\nn = randi([90,numel(all_glo)]) \r\ny_correct = all_glo(n+1)\r\n\r\n%%\r\n% Only for this random test, n and y_correct are displayed but their definition is hidden.\r\nn\r\ny_obtained = H_sequence(n)\r\ny_correct\r\nassert(isequal(y_obtained,y_correct));\r\n\r\n\r\n%%\r\nn = 73\r\ny_obtained = H_sequence(n)\r\ny_correct = 50\r\nassert(isequal(y_obtained,y_correct));\r\n\r\n%%\r\nyy_correct = [0,1,1,2,3,4,4,5,5,6,7,7,8,9,10,10,11,12,13,13,14];\r\nfor n = 0:numel(yy_correct)-1\r\n    y_obtained = H_sequence(n);\r\n    y_correct = yy_correct(n+1);\r\n    assert(isequal(y_obtained,y_correct));\r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":208445,"edited_by":208445,"edited_at":"2024-06-04T13:10:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2024-05-11T17:10:59.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-11T17:04:48.000Z","updated_at":"2026-01-27T21:29:53.000Z","published_at":"2024-05-11T17:10:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Hofstadter H sequence is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$$\\\\begin{cases}\\nH_0 = 0\\\\\\\\\\nH_n = n-H_{H_{H_{n-1}}}\\n\\\\end{cases}$$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first elements of the sequence are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0, 1, 1, 2, 3, 4, 4, 5, 5, 6\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003efor a given\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A005374\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://oeis.org/A005374\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50953,"title":"Round up to π","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 191.35px 7.91667px; transform-origin: 191.35px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo commemorate Pi Day (March 14 in the U.S.), compute the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117.85px 7.91667px; transform-origin: 117.85px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term in a sequence by starting with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.2333px 7.91667px; transform-origin: 62.2333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, rounding up to the next multiple of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n-1\" style=\"width: 35px; height: 18px;\" width=\"35\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.242px 7.91667px; transform-origin: 111.242px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, rounding up to the next multiple of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n-2\" style=\"width: 35px; height: 18px;\" width=\"35\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 171.908px 7.91667px; transform-origin: 171.908px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and so on to rounding up to the next multiple of 1. For example, with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 244.467px 7.91667px; transform-origin: 244.467px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 8, you would get 14, 18, 20, 20, 21, 22, and—the element in the sequence—\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"f(n)\" style=\"width: 32.5px; height: 19px;\" width=\"32.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.6417px 7.91667px; transform-origin: 19.6417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 22. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.325px 7.91667px; transform-origin: 96.325px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"f(n)\" style=\"width: 32.5px; height: 19px;\" width=\"32.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.55px 7.91667px; transform-origin: 15.55px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.517px 7.91667px; transform-origin: 122.517px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term in this sequence. Also compute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n^2/f(n)\" style=\"width: 52.5px; height: 20px;\" width=\"52.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.8417px 7.91667px; transform-origin: 68.8417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and notice its limit as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.1083px 7.91667px; transform-origin: 17.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e gets large. For more on this limit, see \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathpages.com/home/kmath001/kmath001.htm\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003ethis page\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.2167px 7.91667px; transform-origin: 48.2167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by K.S. Brown.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [a,y] = roundUpToPi(n)\r\n  a = f(n);\r\n  y = n^2/a;\r\nend","test_suite":"%%\r\nn = 1;\r\na_correct = 1;\r\ny_correct = 1;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 2;\r\na_correct = 2;\r\ny_correct = 2;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 8;\r\na_correct = 22;\r\ny_correct = 2.909090909090909;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 31;\r\na_correct = 322;\r\ny_correct = 2.984472049689441;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 314;\r\na_correct = 31422;\r\ny_correct = 3.137801540322067;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 3141;\r\na_correct = 3143652;\r\ny_correct = 3.138350237240;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 31415;\r\na_correct = 314162898;\r\ny_correct = 3.141371025295291;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 314159;\r\na_correct = 31416153708;\r\ny_correct = 3.141564629404888;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 3141592;\r\na_correct = 3141592912272;\r\ny_correct = 3.141591087728265;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)\r\n\r\n%%\r\nn = 31415926;\r\na_correct = 314159277765514;\r\ny_correct = 3.141592422344870;\r\n[a,y] = roundUpToPi(n);\r\nassert(isequal(a,a_correct) \u0026\u0026 abs(y-y_correct)\u003c1e-9)   \r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-15T04:19:17.000Z","updated_at":"2026-03-16T11:10:09.000Z","published_at":"2021-03-15T04:33:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo commemorate Pi Day (March 14 in the U.S.), compute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term in a sequence by starting with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, rounding up to the next multiple of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n-1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, rounding up to the next multiple of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n-2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en-2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and so on to rounding up to the next multiple of 1. For example, with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 8, you would get 14, 18, 20, 20, 21, 22, and—the element in the sequence—\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 22. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term in this sequence. Also compute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n^2/f(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en^2/f(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and notice its limit as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e gets large. For more on this limit, see \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathpages.com/home/kmath001/kmath001.htm\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethis page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e by K.S. Brown.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56240,"title":"List numbers that are not squares","description":"The numbers 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, etc. are not perfect squares. Write a function to list the th term in this sequence. Check the test suite to see which functions are banned for this problem. For background music while solving this problem, you can listen to Dave Brubeck’s Unsquare Dance.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 340.408px 8px; transform-origin: 340.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe numbers 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, etc. are not perfect squares. Write a function to list the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.1083px 8px; transform-origin: 31.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term in this sequence. Check the test suite to see which functions are banned for this problem. For background music while solving this problem, you can listen to Dave Brubeck’s \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=lbdEzRfbeH4\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eUnsquare Dance\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = unsquare(n)\r\n  x = setdiff(1:n,(1:floor(sqrt(n))).^2);\r\n  y = x(n);\r\nend","test_suite":"%%\r\nn = 1:100;\r\ny_correct = [2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 46 47 48 50 51 52 53 54 55 56 57 58 59 60 61 62 63 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 101 102 103 104 105 106 107 108 109 110];\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 5075;\r\ny_correct = 5146;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 61086;\r\ny_correct = 61333;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 721097;\r\ny_correct = 721946;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8321008;\r\ny_correct = 8323893;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 94321019;\r\ny_correct = 94330731;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 123456789101112;\r\ny_correct = 123456800212223;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 9e15;\r\ny_correct = 9000000094868330;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nfiletext = fileread('unsquare.m');\r\nillegal = contains(filetext, '*') || contains(filetext, '^') || contains(filetext, 'conv') || contains(filetext, 'setdiff') || contains(filetext, 'prod') || ...\r\n          contains(filetext, '==') || contains(filetext, '~=') || contains(filetext, 'isequal') || contains(filetext, 'pow') || contains(filetext, 'nthroot') || ...\r\n          contains(filetext, 'times') || contains(filetext, 'eq') || contains(filetext, '/') || contains(filetext, 'div') || contains(filetext, 'det');\r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-10-07T03:22:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-07T03:17:26.000Z","updated_at":"2026-03-16T12:45:20.000Z","published_at":"2022-10-07T03:22:08.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe numbers 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, etc. are not perfect squares. Write a function to list the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term in this sequence. Check the test suite to see which functions are banned for this problem. For background music while solving this problem, you can listen to Dave Brubeck’s \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=lbdEzRfbeH4\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eUnsquare Dance\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47310,"title":"Find Logic 15","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 221.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 110.81px; transform-origin: 174px 110.81px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 64\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 25\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 8;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 25;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 216;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":449,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-05T14:25:25.000Z","updated_at":"2026-02-20T09:45:29.000Z","published_at":"2020-11-05T14:25:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 64\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":3010,"title":"Self-similarity 1 - Every other term","description":"Self-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003chttps://oeis.org/selfsimilar.html OEIS page\u003e for more information.\r\n\r\nIn this problem, you are to check if the sequence is self-similar by every other term. The problem set assumes that you use the easiest route: take the first element and then every other element thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\r\n\r\nFor example,\r\n\r\n* seq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]\r\n* seq_every_other = [0,  ,  1, , 1, , 2, , 1, , 2, , 2, , 3, ,] (extra commas are instructional and should not be in the every-other series) \r\n* seq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3]\r\n\r\nSince seq_every_other = seq_orig_first_half, the set is self-similar.\r\n\r\nThis problem is related to \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term Problem 3011\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms Problem 3012\u003e.","description_html":"\u003cp\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003ca href = \"https://oeis.org/selfsimilar.html\"\u003eOEIS page\u003c/a\u003e for more information.\u003c/p\u003e\u003cp\u003eIn this problem, you are to check if the sequence is self-similar by every other term. The problem set assumes that you use the easiest route: take the first element and then every other element thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\u003c/p\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cul\u003e\u003cli\u003eseq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]\u003c/li\u003e\u003cli\u003eseq_every_other = [0,  ,  1, , 1, , 2, , 1, , 2, , 2, , 3, ,] (extra commas are instructional and should not be in the every-other series)\u003c/li\u003e\u003cli\u003eseq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eSince seq_every_other = seq_orig_first_half, the set is self-similar.\u003c/p\u003e\u003cp\u003eThis problem is related to \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term\"\u003eProblem 3011\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms\"\u003eProblem 3012\u003c/a\u003e.\u003c/p\u003e","function_template":"function [tf] = self_similarity_1(seq)\r\n\r\ntf = 0;\r\n\r\nend","test_suite":"%%\r\nseq = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 0, 4, 8, 0, 0, 4, 4, 8, 0, 0, 8, 0, 0, 4, 8, 4, 0, 8, 0, 0, 0, 0, 12, 8, 0, 0, 8, 0, 0, 4, 0, 8, 0, 4, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 4, 12, 0, 8, 8, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, 4, 16, 0, 0, 8, 0, 0, 0, 4, 8, 8, 0, 0, 0, 0, 0, 8, 4, 8, 0, 0, 16, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 4, 0, 12, 8];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 2, 0, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 3, 3, 0, 0, 2, 1, 4, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 4, 0, 1, 2, 0, 3, 0, 4, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 3, 2, 3, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 2, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4, 9, 5, 6, 1, 7, 6, 11, 5, 14, 9, 13, 4, 15, 11, 18, 7, 17, 10, 13, 3, 14, 11, 19, 8, 21, 13, 18, 5, 17, 12, 19];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 6, 6, 30, 6, 30, 30, 54, 6, 102, 30, 78, 30, 78, 54, 150, 6, 102, 102, 126, 30, 270, 78, 150, 30, 150, 78, 318, 54, 174, 150, 198, 6, 390, 102, 270, 102, 222, 126, 390, 30, 246, 270, 270, 78, 510, 150, 294, 30, 390, 150, 510, 78, 318, 390, 390, 54, 630, 174, 366];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 2, 2, 1, 4, 2, 3, 2, 3, 2, 5, 1, 4, 4, 4, 2, 7, 3, 4, 2, 5, 3, 9, 2, 5, 5, 4, 1, 11, 4, 7, 4, 6, 4, 10, 2, 7, 7, 7, 3, 13, 4, 7, 2, 9, 5, 14, 3, 8, 9, 10, 2, 16, 8, 9, 5, 9, 5, 21, 1, 11, 11, 10, 4, 17, 7, 10, 4, 11, 6, 11, 4, 16, 10, 11, 2, 23, 7, 12, 7, 14, 7, 20, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 0, 2, 1, 1, 1, 0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 1, 2, 0, 0, 2, 1, 1, 2, 1, 1, 1, 1, 0, 2, 0, 0, 2, 2, 1, 2, 0, 1, 2, 0, 1, 3, 0, 0, 2, 1, 0, 2, 2, 1, 1, 0, 0, 3, 1, 2, 2, 1, 0, 2, 0, 1, 2, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 24, 24, 96, 24, 144, 96, 192, 24, 312, 144, 288, 96, 336, 192, 576, 24, 432, 312, 480, 144, 768, 288, 576, 96, 744, 336, 960, 192, 720, 576, 768, 24, 1152, 432, 1152, 312, 912, 480, 1344, 144, 1008, 768, 1056, 288, 1872, 576, 1152, 96, 1368, 744, 1728, 336];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 0, 2, 1, 1, 1, 0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 1, 2, 0, 0, 2, 1, 1, 2, 1, 1, 2, 1, 0, 2, 0, 0, 2, 2, 1, 2, 0, 1, 2, 0, 1, 3, 0, 0, 2, 1, 0, 2, 2, 1, 1, 0, 0, 3, 1, 2, 2, 1, 0, 2, 0, 1, 2, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 2, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 1, 2, 2, 0, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 3, 3, 0, 0, 2, 1, 4, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 4, 0, 1, 2, 0, 3, 0, 4, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 3, 2, 3, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 0, 4, 8, 0, 0, 4, 4, 8, 0, 0, 8, 0, 0, 4, 8, 4, 0, 8, 0, 0, 0, 0, 12, 8, 0, 0, 8, 0, 0, 4, 0, 8, 0, 4, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 4, 12, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 4, 16, 0, 0, 8, 0, 0, 0, 4, 8, 8, 0, 0, 0, 0, 0, 8, 4, 8, 0, 0, 16, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 4, 0, 12, 8];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, -1, 0, 1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -3, -2, 1, -1, 2, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, 1, -4, -3, 1, -2, 3, 1, -2, -1, 3, 2, -1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -1, 0, 1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -5, -4, 1, -3, 4, 1, -3, -2, 5, 3, -2, 1, -3, -2, 1, -1, 4, 3, -1, 2, -3, -1, 2, 1, -3, -2, 1, -1, 2, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3, 2, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 7, 6, 6, 5, 6, 5, 5, 4, 6, 5, 5, 4, 5, 4, 4, 3, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 24, 24, 96, 24, 144, 96, 192, 24, 312, 144, 288, 96, 336, 192, 576, 24, 432, 312, 480, 144, 768, 288, 576, 96, 744, 336, 960, 192, 720, 576, 768, 24, 1152, 432, 1152, 312, 912, 480, 1344, 312, 1008, 768, 1056, 288, 1872, 576, 1152, 96, 1368, 744, 1728, 336];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 4, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 16, 16, 8, 16, 16, 32, 8, 8, 16, 32, 16, 32, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 6, 6, 30, 6, 30, 30, 54, 6, 102, 30, 78, 30, 78, 54, 150, 6, 102, 102, 126, 30, 270, 78, 150, 30, 150, 78, 318, 54, 174, 150, 198, 6, 390, 102, 270, 102, 222, 126, 390, 30, 246, 270, 270, 78, 510, 150, 294, 30, 390, 150, 510, 78, 318, 318, 390, 54, 630, 174, 366];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 6, 5, 5, 4, 5, 3, 4, 3, 5, 4, 4, 3, 4, 3, 3, 2, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 7, 6, 6, 5, 6, 5, 5, 4, 6, 5, 5, 4, 5, 4, 4, 3, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 2, 2, 1, 4, 2, 3, 2, 3, 2, 5, 1, 4, 4, 4, 2, 7, 3, 4, 2, 5, 3, 9, 2, 5, 5, 5, 1, 11, 4, 7, 4, 6, 4, 10, 2, 7, 7, 7, 3, 13, 4, 7, 2, 9, 5, 14, 3, 8, 9, 10, 2, 16, 5, 9, 5, 9, 5, 21, 1, 11, 11, 10, 4, 17, 7, 10, 4, 11, 6, 18, 4, 16, 10, 11, 2, 23, 7, 12, 7, 14, 7, 20, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, -1, 0, 1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -3, -2, 1, -1, 2, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, -1, -4, -3, 1, -2, 3, 1, -2, -1, 3, 2, -1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -1, 0, 1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -5, -4, 1, -3, 4, 1, -3, -2, 5, 3, -2, 1, -3, -2, 1, -1, 4, 3, -1, 2, -3, -1, 2, 1, -3, -2, 1, -1, 2, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4, 9, 5, 6, 1, 7, 6, 11, 5, 14, 9, 13, 4, 15, 11, 18, 7, 17, 10, 13, 3, 14, 11, 19, 8, 21, 13, 18, 5, 17, 12, 19];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":72,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":30,"created_at":"2015-02-13T04:04:32.000Z","updated_at":"2026-03-16T14:11:36.000Z","published_at":"2015-02-13T04:04:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/selfsimilar.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOEIS page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more information.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, you are to check if the sequence is self-similar by every other term. The problem set assumes that you use the easiest route: take the first element and then every other element thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_every_other = [0, , 1, , 1, , 2, , 1, , 2, , 2, , 3, ,] (extra commas are instructional and should not be in the every-other series)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince seq_every_other = seq_orig_first_half, the set is self-similar.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is related to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3011\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3012\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45384,"title":"Sum! Sum! Sum!","description":"Calculate the sum of the sequence up to nth term \u003e\u003e \r\n\r\n  a,aa,aaa,aaaa,... \r\n  2,22,222,2222,...  [for a=2]","description_html":"\u003cp\u003eCalculate the sum of the sequence up to nth term \u0026gt;\u0026gt;\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ea,aa,aaa,aaaa,... \r\n2,22,222,2222,...  [for a=2]\r\n\u003c/pre\u003e","function_template":"function  y = series_sum(a,n)","test_suite":"%%\r\nassert(isequal(series_sum(3,4),3702))\r\n%%\r\nassert(isequal(series_sum(2,15),246913580246910))\r\n%%\r\nassert(isequal(series_sum(9,9),1111111101))\r\n%%\r\nassert(isequal(series_sum(1,12),123456790122))\r\n%%\r\nassert(isequal(series_sum(5,5),61725))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-03-24T13:05:35.000Z","updated_at":"2026-03-05T07:10:14.000Z","published_at":"2020-03-24T13:05:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the sum of the sequence up to nth term \u0026gt;\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[a,aa,aaa,aaaa,... \\n2,22,222,2222,...  [for a=2]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44544,"title":"Normie Function (2)","description":"Another _Normie Function_ defined as _f(n)= f(n-1)+f(n-2)+f(n-3)_ , *when n\u003e3* and _1_ , *when n\u003c=3*. *Find the nth term of this function* .","description_html":"\u003cp\u003eAnother \u003ci\u003eNormie Function\u003c/i\u003e defined as \u003ci\u003ef(n)= f(n-1)+f(n-2)+f(n-3)\u003c/i\u003e , \u003cb\u003ewhen n\u0026gt;3\u003c/b\u003e and \u003ci\u003e1\u003c/i\u003e , \u003cb\u003ewhen n\u0026lt;=3\u003c/b\u003e. \u003cb\u003eFind the nth term of this function\u003c/b\u003e .\u003c/p\u003e","function_template":"function y = normie(n)\r\n  y = n;\r\nend","test_suite":"%%\r\nn = 3;\r\ny_correct = 1;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 23;\r\ny_correct = 289329;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 36;\r\ny_correct = 797691075;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 37;\r\ny_correct = 1467182629;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 40;\r\ny_correct = 9129195487;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 50;\r\ny_correct = 4045078385041;\r\nassert(isequal(normie(n),y_correct))\r\n%%\r\nn = 70;\r\ny_correct = 794174268033812736;\r\nassert(isequal(normie(n),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":104442,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2018-03-28T11:02:45.000Z","rescore_all_solutions":false,"group_id":61,"created_at":"2018-03-22T09:27:39.000Z","updated_at":"2026-03-16T11:16:28.000Z","published_at":"2018-03-22T09:27:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnother\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNormie Function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e defined as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef(n)= f(n-1)+f(n-2)+f(n-3)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhen n\u0026gt;3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhen n\u0026lt;=3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFind the nth term of this function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45253,"title":"Pell numbers ","description":"Find the nth pell number\r\n\r\n\r\n\u003chttps://en.wikipedia.org/wiki/Pell_number\u003e","description_html":"\u003cp\u003eFind the nth pell number\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Pell_number\"\u003ehttps://en.wikipedia.org/wiki/Pell_number\u003c/a\u003e\u003c/p\u003e","function_template":"function p=pell_seq(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nn = 3;\r\ny_correct = 2;\r\nassert(isequal(pell_seq(n),y_correct))\r\n%%\r\nn = 6;\r\ny_correct = 29;\r\nassert(isequal(pell_seq(n),y_correct))\r\n%%\r\nn = 9;\r\ny_correct = 408;\r\nassert(isequal(pell_seq(n),y_correct))\r\n%%\r\nn = 12;\r\ny_correct = 5741;\r\nassert(isequal(pell_seq(n),y_correct))\r\n%%\r\nn = 15;\r\ny_correct = 80782;\r\nassert(isequal(pell_seq(n),y_correct))\r\n\r\n%%\r\nn = 19;\r\ny_correct = 2744210;\r\nassert(isequal(pell_seq(n),y_correct))\r\n\r\n%%\r\nn = 23;\r\ny_correct = 93222358;\r\nassert(isequal(pell_seq(n),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":77,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-03T18:34:11.000Z","updated_at":"2026-01-16T23:48:17.000Z","published_at":"2020-01-03T18:35:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the nth pell number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Pell_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Pell_number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":51002,"title":"Deduce the pattern behind the sequence","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 917.917px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 458.958px; transform-origin: 407px 458.958px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60.075px 7.91667px; transform-origin: 60.075px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHere's a sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.075px 7.91667px; transform-origin: 37.075px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTricky? Not!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46.6px 7.91667px; transform-origin: 46.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou'll deduce it\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 7.91667px; transform-origin: 44.3333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFrom this plot.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49px 7.91667px; transform-origin: 49px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf the plot gives \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.0917px 7.91667px; transform-origin: 44.0917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou the blues,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.5667px 7.91667px; transform-origin: 64.5667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe test suite should\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0167px 7.91667px; transform-origin: 63.0167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eProvide some clues.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.9167px 7.91667px; transform-origin: 52.9167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFeeling anxious?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.15px 7.91667px; transform-origin: 41.15px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou'll be fine.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.1167px 7.91667px; transform-origin: 52.1167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe code I wrote\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.3417px 7.91667px; transform-origin: 51.3417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIs one short line.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 497.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 248.958px; text-align: left; transform-origin: 384px 248.958px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 657px;height: 492px\" 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\" data-image-state=\"image-loaded\" width=\"657\" height=\"492\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = mysterySeq(n)\r\n  a = f(n);\r\nend","test_suite":"%%\r\nassert(isequal(mysterySeq(2),2))\r\n\r\n%%\r\nassert(isequal(mysterySeq(4),4))\r\n\r\n%%\r\nassert(isequal(mysterySeq(9),6))\r\n\r\n%%\r\nassert(isequal(mysterySeq(15),8))\r\n\r\n%%\r\nassert(isequal(mysterySeq(36),10))\r\n\r\n%%\r\nassert(isequal(mysterySeq(35),12))\r\n\r\n%%\r\nassert(isequal(mysterySeq(144),14))\r\n\r\n%%\r\nassert(isequal(mysterySeq(256),16))\r\n\r\n%%\r\nassert(isequal(mysterySeq(315),18))\r\n\r\n%%\r\nassert(isequal(mysterySeq(441),20))\r\n\r\n%%\r\nassert(isequal(mysterySeq(495),22))\r\n\r\n%%\r\nassert(isequal(mysterySeq(143),24))\r\n\r\n%%\r\nassert(isequal(mysterySeq(169),26))\r\n\r\n%%\r\nassert(isequal(mysterySeq(115),28))\r\n\r\n%%\r\nassert(isequal(mysterySeq(4802),30))\r\n\r\n%%\r\nassert(isequal(mysterySeq(65536),32))\r\n\r\n%%\r\nassert(isequal(mysterySeq(62500),34))\r\n\r\n%%\r\nassert(isequal(mysterySeq(186),36))\r\n\r\n%%\r\nassert(isequal(mysterySeq(361),38))\r\n\r\n%%\r\nassert(isequal(mysterySeq(1048576),40))\r\n\r\n%%\r\nassert(isequal(mysterySeq(117649),42))\r\n\r\n%%\r\nassert(isequal(mysterySeq(14641),44))\r\n\r\n%%\r\nassert(isequal(mysterySeq(529),46))\r\n\r\n%%\r\nassert(isequal(mysterySeq(116875),48))\r\n\r\n%%\r\nassert(isequal(mysterySeq(301),50))\r\n\r\n%%\r\nassert(isequal(mysterySeq(235),52))\r\n\r\n%%\r\nassert(isequal(mysterySeq(329),54))\r\n\r\n%%\r\nassert(isequal(mysterySeq(159),56))\r\n\r\n%%\r\nassert(isequal(mysterySeq(517),58))\r\n\r\n%%\r\nassert(isequal(mysterySeq(3486784401),60))\r\n\r\n%%\r\nassert(isequal(mysterySeq(444125),62))\r\n\r\n%%\r\nassert(isequal(mysterySeq(96049800),64))\r\n\r\n%%\r\nassert(isequal(mysterySeq(31381059609),66))\r\n\r\n%%\r\nassert(isequal(mysterySeq(533715),68))\r\n\r\n%%\r\nassert(isequal(mysterySeq(282475249),70))\r\n\r\n%%\r\nassert(isequal(mysterySeq(36501),72))\r\n\r\n%%\r\nassert(isequal(mysterySeq(1369),74))\r\n\r\n%%\r\nassert(isequal(mysterySeq(130321),76))\r\n\r\n%%\r\nassert(isequal(mysterySeq(46023),78))\r\n\r\n%%\r\nassert(isequal(mysterySeq(576650390625),80))\r\n\r\n%%\r\nassert(isequal(mysterySeq(1172889),82))\r\n\r\n%%\r\nassert(isequal(mysterySeq(13841287201),84))\r\n\r\n%%\r\nassert(isequal(mysterySeq(22755),86))\r\n\r\n%%\r\nassert(isequal(mysterySeq(2133),88))\r\n\r\n%%\r\nassert(isequal(mysterySeq(8033333),90))\r\n\r\n%%\r\nassert(isequal(mysterySeq(267),92))\r\n\r\n%%\r\nassert(isequal(mysterySeq(102656268),94))\r\n\r\n%%\r\nassert(isequal(mysterySeq(16168),96))\r\n\r\n%%\r\nassert(isequal(mysterySeq(228125),98))\r\n\r\n%%\r\nassert(isequal(mysterySeq(1125899906842624),100))\r\n\r\n%%\r\np = primes(1e4); k = randi(length(p));\r\nassert(isequal(mysterySeq(p(k)),p(k)))\r\n\r\n%%\r\nassert(isequal(mysterySeq(mysterySeq(mysterySeq(mysterySeq(mysterySeq(mysterySeq(50014)))))),5))","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2021-03-18T00:35:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-17T02:24:34.000Z","updated_at":"2025-12-15T15:32:30.000Z","published_at":"2021-03-17T02:29:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere's a sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTricky? Not!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou'll deduce it\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFrom this plot.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the plot gives \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou the blues,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test suite should\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProvide some clues.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFeeling anxious?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou'll be fine.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe code I wrote\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIs one short line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"492\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"657\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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ZmSgsDAQLW9I5MCo0WLFukl1+JSlfnyFPHzzz+r4FB6Y8sA4lI0LRcXKTkIDQ1V20kQKR1tJGi0JkFVXl6e6lzzX+TpxNFJfp3pGcOFnpeIzomznfvOwpH2y7S1+3H4M/OBSgWQwg1Y3wJPTE9Aifmfm7noDMeYo9egnCuXCSLlYJWSKBkDUkoT77nnnn9LFZcsWaKKpZs3b662bdOmDeLi4pCVlaWWLWQbGfpHOt0QERFR2WLSzPvnIZtaLMMTWeu8UAxDtZckx+cyQeT+/ftx8cUXq+DRmqT/+OOPqlrb0htbBhrftm0bfv/9d7VsIR1tJJAcMmSITiEiIiJbnWqGAPWO6SWtSpGZVtqhhuXczsFlgsiGDRti1KhRqi2jVGdLu0jpHCNtIaWdycSJE/WWpSWR0kv7hRdeUD2uNmzYoKq+J0yYoNJlPREREZXtxrYRQK9D5ruC0gTRbjceurkGPOGOEjaXcAou1SZy0qRJGDhwoCqNHDZsmJpHW3off/fdd2roFwup4n7zzTfRrVs33HTTTWpbKZ3s27ev6oUlPa2JiIiobGE+3vjluQZo+/xOYPAKYPTfeHWKP968spFazxjSObhUEClmzpypOswsXbpUDcchQ/5IT2xb0nnmm2++UR1sZExI+R0Z/9EZepIRERFdaAOahGPTi21hLLwYxufd8Hjv+mYqW0M6E5cLIi1k5hkZTPe/yBAX0pFGenYTERERUSmXDSKJiIiI6OwxiCQiIiKicmMQSURERETlxiCSiIiIiMqNQSQRERERlRuDSCIiIiIqNwaRRERERFRuDCKJiIiIqNwYRBIRERFRuTGIJCIiIqJyYxBJREREROXGIJKIiIiIyo1BJBERERGVG4NIIiIiIio3BpFEREREVG4MIomIiJzYRxsPotE7i3HRZyuxaF+8TiU6dwwiiYiInFB2QTGGz9yEu0bnYd8D/bDqlp4Y0jcH13+9RW9BdG4YRBIRETmhJYcS8eNMX2BnM51iOtQQcz53xz9HU3QC0dljEElEROSEolOygd1heum4kvUhSMoo1ktEZ49BJBERkRNqWyMIXi1S9ZKVJklw9zT0AtHZYxBJRETkhLpHhKLtwAzAO12nmBocQN8RQO96VXUC0dljEElEROSEfN098PkdTTFkchxw+V/qdfvLuVh4X0u1juhcMYgkIiJyUk1DA/DTg81h/HiRek2/tjkDSDpvGEQSERERUbm5ZBD51ltv4eqrr8aVV16JGTNm6NST7du3D/fddx8GDRqEBx98ELGxsXoNERERkWtzqSAyLS0N9erVw5tvvgk3NzeV9uKLL6JJkybIyspSyxZffvklOnTogK1btyI0NBTr1q1DVFQU5syZo7cgIiIicl0uFUQ+//zzKnj84osv8O2332LevHmYPn06iouL8cwzz+itgJSUFDz33HMYMmQIli9frgLKVatWoV+/fpg8eTKOHDmityQiIiJyTS4TREpJ486dO1GrVi307NlTpwK9e/dGixYtVLBo8euvvyI5ORljxozRKaXeeOMNbNy4EWvWrNEpRERERK7JZYLIgIAAhISEIDMzU5U8WkhwKdXcYWHHR/WfP38+WrdujYiICJ1SKjIyUqUvWbJEpxARERG5JpeqzpaSxYKCAtVZZuXKlfjrr79UNbZUT0+YMEFvBezdu1eVWErQaUuCzT179uilUwsKCtLvHFeVKlXUy1m4u7vrd47PmfYL82J/5FxxlvPFma5jzrRfnCUvznT9Ohtuhkm/dwmffPIJHn74Yfj4+Kj2kVIqOWXKFNx44416C6jON1LlLe0lfX19dSpUAHr55ZejqKgIf/75p049mXS+efLJJxEeHo6SkhL1Cg4OVm0wMzIy9Fb2Tz53YmKiCqjlvSOTfS2966V02dHzIhetw4cPq5Jx5sV+OEteJB8JCQnqQdjLy0unOiY576WNu1zH5ZrvCHw8qiA0wB2ennJ/MpCZU4Ks/GIYcFO1Zp6envD394cj37plv8i9UH4GBgY6TF78/PxUvLBgwQJ4e3urz19YWKhqKGfPnq23ci0uFUQ+9dRT+OCDD9RwPaNGjVIXy88++0wN+SOdbp544gm1Xd26ddGrVy8VRFpfeCSIHD58uPp5uiBSfk9uJAMGDNApjis+Ph41a9bUS44tLi4OtWvX1kuOTUrPbZtbOCrmxf5Im3CpiXGGkqLU1FQVdDlKQLw1KQuD3tiF2PW58Gngg9dviMR9F5degyXwknw4SkB8OtnZ2eqn7BtHN3jwYCxatEgvuRaXKYddu3atKiG89dZb1bA+MlxP06ZN8dJLL+Huu+/GO++8gx07dqht5aCWpwvb0gSJtyXdw+O/R/t3pBLHU5H8O3rpkDXrtrCOzpn2C/Nif+RccZbzxZGuY2viUtH2oZ2IndIc+P1i5H3UGfffnY5nf96r1peUOM9+cZZjzJmuX2fDZYJIGThcqjOvvfZanXLcNddcowLELVu2qOVmzZqpaoPc3Fy1bC0nJwd16tTRS0REROfHhxsOwfg2CiiwKp3b0QSvfJ2s3rqZ/xHZE5cJIqXqWkoQJQi0JWmW9ULGg9y1a5dqD2hNAsu///4b3bt31ylERETnR0ZBAZAfqJcsqqB4O4NHsk8uE0S2a9cOjRo1UtXWtqRBrASRMkONkPYNEjDKIOPWXn/9ddXp5qKLLtIpRERE50ePiKpAZJxe0rzygPZmcElkh1wmiJSpDe+55x4sXLgQV1xxBd5//301b7bMoT1r1iw89thjaNiwodq2cePGaluZHlGGBZJgUoYF+vDDD3HDDTeowcmJiIjOp4e7NAL6RpvvSjudAAbQfy2+uK/03uRC/WDJQbhMECkkMPztt99U7+qPPvoI06ZNQ35+vkqTINHaK6+8gqlTp6rZaeT9+vXrVSmm9XiSRERE51PmjIvwzLJDaPPRMoz4bh0Oft0R17erpdYxhCR743LjRFqkp6erp7qyBhS3JW0jZczHMyVD/Mi4kCNHjtQpjkl6nckQP84yLI5lDD9ncOjQITUUlTNgXuyPjBMp10ZHHydSyHBFMuKGMwyLI8MVyT5xhmFxLCOYOPrEHHKfHDp0KIf4cTUS5J1JACnKE0ASERERuQKXDSKJiIiI6OwxiCQiIiKicmMQSURERETlxiCSiIiIiMqNQSQRERERlRuDSCIiIiIqNwaRRERERFRuDCKJiIiIqNwYRBIRERFRuTGIJCIiIqJyYxBJREREROXGIJKIiIiIyo1BJBERERGVG4NIIiIiIio3BpFEREREVG4MIomIiKzklBSi6+sb4NZ/KdyuXomx3+5DvlGk1xKRBYNIIiIibX9qDrq+vBlrXqoLLO4DfN8TUx70xsjpO1FQUqK3IiLBIJKIiEj781Aitn1RA0gL0ymmo3WwYK4Hdqdm6AQiEgwiiYiItMTsAvN/AXrJSrQXMrJZEklkjUEkERGR1rFWMDw6JOglKx3TEODrrheISDCIJCIi0i5rUB3tL08DfBJ1iqnXGtw7OgBtw4N1AhEJBpFERERW1tzfFVNXZKLLJyvQfeZKrPi8Ed69qpleS0QWDCKJiIhsPNipIf659WKsurknekZW06lEZI1BJBERuYx1R9PQYNqf6P7pSrz2d7ROJaKz4TJBZEFBAY4dO6ZeCQkJJ7wkLT4+Hrm5uXrrUsXFxdi/fz927NiBAwcOwDAMvYaIiByFmxsgV++xC/ag8617cODB/vj7tp54vF8omr++qnQjIio3lwki165di+HDh2PAgAEYOHDgv69BgwbhyiuvxIgRI/Drr7/qrYGkpCQ8+uij6NatGzp06IAePXrgscceQ3Jyst6CiIgcgUcVNxzOysG0WXnAr511qik3DLu+qYHpmw/qBCIqD5cJImvWrIlhw4bhqquuUkGjvK6++mqMGjUKJSUliImJQb169fTWwLhx4zB9+nTMmjUL0dHRmDp1Kt59911MnDhRb0FERI7A3c0NMSnZKNwv4z+6lSZabKiBA/EFeoGIysNlgshGjRrh6aefxvPPP4/nnntOvZ555hnUqVMHe/bswezZs9G+fXu1rZRaSsD41VdfqZLLyMhIjBw5Um3z8ccfY8WKFWo7IiKyf8UlBqLCAlC1qTRZshkwvHk8vHzYVInobLh0x5qDBw/i8ccfV6WSl156qU4Fvv/+ezRt2lS9rA0ePBje3t4qyCQiIsdQZBio7eeLywebt7yIWJ1qCkxB7aHJuLvz8VooIjpzLh1EShtHX19fFUha27p1K5o0aYLq1avrlFJVqlRBVFQUVq9erVNOLSgoSL9zXJJfeTkLd3fnmW3CmfYL82J/5FxxlvNF9ombW+l+eW1EYzw6rRi46h9g+GpcNO4wto/viOp+3mq9vXOm/eIseXGm69fZcDNctMvxn3/+qdpHStvHhx9+WKeWql+/vupIM2PGDBVkWuTn56t2ldJr+48//tCpJ5szZw6efPJJhIeHq/aW8goODsa8efOQkeE4E/jL505MTEStWrXUe0fm5uaG2NhYREREOHxe5KJ1+PBh1cyCebEfzpIXyYeMWiEPwl5eXjrVMcl5n5KSoq7jPj4+qoNNoE8VBPhKYAnk5RtIzSlGYbH93wYlL2lpafD09IS/v79DjxYieZF7ofwMDAx0mLz4+flhypQpWLBggaqVlM9fWFiI1q1bq+Zurshlg8gbb7xRVUuvXLkSYWFhOrVU3bp10atXL9WxRi48FjJMkPTwlmBy8eLFOvVk8ntyI5H2lI5Ohj6STknOIC4uDrVr19ZLju3IkSMqIHYGzIv9kVEoQkJCnKKkKDU1VQVdjh4QCwm8JB/W9yVHlZ2drX7KvnF00tRt0aJFesm1uGQ57JYtW7Bu3Tr07dv3pADSQkoSbONrWZbXmRRfO1KJ46nId+DopUPWpATZWTjTfmFe7I+cK85yvjjTdcyZ9ouz5MWZrl9nwyWDyGXLlmHXrl146qmndMqJpDo7JydHFVNbkwAyLy/PKdo7EhEREZ0LlwsiJTD866+/VMcZqbYuS7t27XD06FGkp6frlFISRO7duxctWrTQKURERESuyeWCSJnaUNpCykw1p9K/f39s2rRJtQe0JtMfSpsnmcWGiIiIyJW5XBApvQ737dunpjI8lSFDhqhA8aabblJzZkv7RhlTUqZGlFlu+vTpo7ckIiIick0uF0RKhxpxqqps4eHhoaY5DA0NRdeuXVVQKbPZyLSIMiRQQIBMnUVERETkulwuiBw4cCA2bNiggsPTkXaRCxcuxCeffKJKID///HM1k02rVq30FkRERESuy+WCSBn7TEoVZdDQ/yIlkVIKOWbMGDUOVNWqVfUaIiK60DKLCtHu5XVw678UbiNW4qkf96MQzjNUF5Gjc7kgkoiI7F90SjY6TtyMzS83BBb3Ab7riVfud8f1M3eh2HDtsfmI7AWDSCIisju/7EtA9Oe1gEyrGqDDdfHtHDfsyyid7YSIKheDSCIisjuJuflAcqBesrLHA9l5LIkksgcMIomIyO50qhmCKu1PHKsXMIAOGfD34q2LyB7wTCQiIrszrElNNB+aDHim6BRT33/w6M3BaBJaRgklEVU4BpFERGSXtj3SHa+vTEbnT1bgos9W4p8vmuG1oU30WiKqbAwiiYjIbo3t0gRrbr0YK2/qiS61QnUqEdkDBpFEREREVG4MIomIiIio3BhEEhEREVG5MYgkIiIionJjEElERERE5cYgkoiIiIjKjUEkEREREZUbg0giIiIiKjcGkURERERUbgwiiYiIiKjcGEQSERERUbkxiCQiIiKicmMQSURERETlxiCSiIiIiMqNQSQRERERlRuDSCIiIiIqNwaRRER0Ejf9M98oxoPzd8OtzxK4XbUCl765DRlFBXotEbkylwwi9+7di88++wzvvPMOfvzxR+Tm5uo1J0pJScHXX3+NadOmYc6cOcjIyNBriIicm3sVN2QUFOHKD3Zg2lNewLK+wLyL8ccTddH55U1Izs3XWxKRq3K5IHL69OkYMGAA7r33Xjz55JO49dZb1XJhYaHeolR0dDRGjBiB2267DU8//TRuv/12XHHFFYiJidFbEBE5ryrubohJy8TPX5sB5K4GOtVUGIQ939TAon0JOoGIXJVLBZE//PADHnzwQVxzzTXIzs5GVlYWfv31V8TGxmLgwIF6K6h1o0ePRnp6OnJycpCZmYn4+HgcO3YMd955J1JTU/WWRETO63BGPpDho5es7PdHXGKxXiAiV+UyQWRxcbEqhezcuTMmTZqkU4FOnTrhlltugaenJ9LS0lTaypUrsXXrVrzxxhtqWQQEBODDDz/E6tWr8c8//+hUIiInZQCtqweieuvs0gVrneNRs6q7XiAiV+UyQeT27duxZ88eVcJoS6q1Z8+ejaCgILW8YMECNGnSBBEREWrZomPHjggPD8f69et1yqlJUOro3Nzc1MtZOFNeiC4kOVeKSoCGQf646irzvGm0T68xNYlBj6vzcHObSJ1AFcWZrsnOkpcqVVyya8m/3AyTfu/UpCpbAsgNGzagpKREBY0SWHbt2hXXXXcdGjQ43ubnoosuQp06dTBz5kz4+fnpVCA/Px+DBg1SAaJUg5+KdNqRKvLBgwer35Gv2MPDA+3atUNRUZHeyv7J9yRV+PJdyHtHJherw4cPo27dug6fF7loHThwAPXr12de7Iiz5EXyIc13QkJC4OvjDU93N8zbcxQTVsSgpLhEBY8PXxSFgvw8lNj53UPO+6SkJPj7+8PHp4xqeQcieZGmVHL/kZoxR751S16kuZj8lMIbR8mLu7s7Dh48iMTERHWeyEv6U0yePBnz58/XW7kWlwkiv/jiC/zvf/9TVdRvvvkmoqKiEBwcjCVLlsDb2xvffPMN2rdvr7aVm0CPHj0wY8YM+Pr6qjRRUFCAyy+/XFWN//HHHzr1ZPJvzZs3D23btlVBo9xQJBgdM2bMKXuC2yP53AkJCahdu7bD3+DlYnXkyBFERkY6RbBy6NAhpwmImZfK42UGiIG+HuY7N/NaVYLMfPMh162KeniU66OXl5ca6sfXswp8vUurrwsKZTvHaA8p531ycrK6/jpDEClNrqRAwhmCSMtoJ44URMr58Msvv2Djxo0qmJd8SBApHXHnzp2rt3ItLhNEzpo1C4888ghq1qyJl156CUOGDFEX/XXr1qme1/LUvWLFCrWt3AR69+6Njz/++IQLjwSRw4cPV6WLixcv1qknk7aX8u8MHTpUpziuo0ePolatWnrJsUnpsJSqOgMpVZWA2BkwL5UnNjsX13yzCXklRRjcuDom9Gqm0qX0Tq6JErA4OhmqTUoipbDA0UnpnQQy1oUbjko6tgoJiB2d1DouWrRIL7kWl6nMl4AxLy9PlSRKICgXR0nr0qWLGu5HqqEsVdRyksrThW1pgsTbUrJ4JhdWRypxPBXJvzM9Yzh6SZc1Z9ovzEvleHf1YUTctBmrbu2ODbdfjImX1ITbTcvUOjcYTnO+yD5xlmNM9omz7BdnyYuz7I+z5TJBpOXJrUOHDuqntZYtW6qfluL1xo0bq2F9pMTRmlyIJBCVzjVERI7s6dnxwDyr62FhMPBbC4xdvBOBuuqaiOh0XCaIrF69OkJDQ1VbH1sSMAppNCvatGmDuLi4f4vbLaTkUob+kfaURESOKq0wHxmx5vXO8NIp2rFwbNmbD08PjmRARP/NZYLIbt26qY4zMtajbfHzd999h8DAQPTr108tSy/ubdu24ffff1fLFtLRRgJJaU9JROSoQjy9Ub+RGShWsZkDOywJPkHFMFy7ho6IzpDLBJHSk0p6R0tJpAwuvmzZMqxduxYvvPACvv/+e9x9992qIbmQkshrr71WrZMeVzIskMydPWHCBJUu64mIHNndl1cFovbrJZNXNtArGtMGt3CY3tdEVLlcJogU/fv3xyeffKICSOlcI51s3nrrLYwdO1ZNh2gh3fZlGCApvbzpppswbNgwVTrZt29fNR6UM/RYJCLXNqZXBMa/4Q2PW9YAg5aj+ZO7sGpqFOoH+iJfRhonIvoPLhVEChl2RwYLlXGdVq1apYZMeO655/Ta46TzjIwdKe0lZUxI6WQj4z9KtTcRkaPzcXfHcwPro/DTLjAW9cKOFzuie0SoXktE9N9cLoi0kCCxYcOGeunUpBpcOtJYOt0QERERkQsHkURERER09hhEEhEREVG5MYgkIiIionJjEElERERE5cYgkoiIiIjKjUEkEREREZUbg0giIiIiKjcGkURERERUbgwiiYiIiKjcGEQSERERUbkxiCQiIiKicmMQSURERETlxiCSiIiIiMqNQSQRERERlVulBJHLly/HtGnT8NJLL+HZZ5/Fk08+ieeeew6TJk3CBx98gM2bN+stiYiIiMgeVWgQuWjRIlx66aUYPXo0HnzwQRU4vv322/joo4/w+uuv45lnnsF9992Hq6++Wm23a9cu/ZtERM6pGCW49tv1aP7+Uvxv0WZklxTqNURE9q1CgsidO3eiVatWuP/+++Hr64vnn38ehmGgpKQEGRkZSElJQW5urkqTn/feey+8vLzQo0cPFUzu3r1b/yUiIuex5kgaPG5dhbnXNcOue/vg4yFNEHDZOmw+lqG3ICKyXxc8iNyyZQsuv/xyDBs2DMuWLcOPP/6IO++8U689mQSPjzzyCBYuXIgffvgBLVu2RO/evVFYyKdzInIuTy/aB3zdBigO0Cl+wF+tcfNnfHAmIvt3wYPIevXqqWBQ2jtGRkbq1DNz8cUX46233sLvv/8ONzc3nUpE5AwMHEjKB/KC9LKWF4DNW4r1AhGR/brgQWRwcLAqTTwXrVu3hoeHh14iInIGbugY6Q9421Rd++bAq4YZXBIR2bkK7VhDRETHPdw3Eui413xnlCagGOi8E5/d2EwvExHZr0oJIrdu3YrBgwejf//+Zb46d+6s2lISETmzbhGheO/1cEQ8tAm4bDnCHtyIL96ujeva1dRbEBHZrwoPIqVzzaBBg7Bv3z54e3urjjS2L0lnG0gicgX3dI/A4Tfbw/i1FxKndsL1bWvpNURE9q3Cg8hNmzYhMTER8+fPV+NG/vzzzye9Vq5cqdpBEhEREZF9qvAgMicnBzVq1EBUVJROqVgyI44McD516tR/X2+++SY+/vhjvcVxUloqg59LyakMjh4bG6vXEBEREbm2Cg8i/fz8kJ2drZcq3hNPPIE33ngDn3zyiQoc5fXhhx/iyy+/1FuUkuUOHTqo9puhoaFYt26dCnznzJmjtyAiIiJyXRUeRI4YMQK1atXC3LlzdUrF2bNnDwICAvDQQw/hjz/+UNXp8vr1118xa9YsvRXUDDoyJeOQIUPUPN8SUK5atQr9+vXD5MmTceTIEb0lERERkWuq8CDy0KFDqFmzpgrkhg4dipEjR+L666//9zVq1Cg1w41MlXi+SY9v6bgj0ymGh4ejbt266iUDolsPhC5BZXJyMsaMGaNTSkkJ5saNG7FmzRqdQkREROSaKjyIPHDggJovu0WLFsjMzMSxY8dUyZ71SwLN/PzzP9juhg0bEBQUhObNm6vOPTExMUhKStJrj5NOP9KxJyIiQqeUkkBT0pcsWaJTiIiIiFxThQeR1113HVavXo3ffvtNBWNLly494SVDAK1fvx7t2rXTv3H+7N27F8XFxRg/fryaUrFjx4646qqr1JSM1mQ7qXIPCQnRKceFhYWpavH/IsGqo6tSpYp6OQt3d3f9zvE5035hXuyPnCvOcr4403XMmfaLs+TFma5fZ8PNMOn3Tk2qp6+88kpVpS3V6Pfeey9yc3Px+uuvq3aPDzzwAF555RW1rVRv9+zZE9OnT4evr69KEwUFBaqqvaioCH/++adOPZl0vnnyySdVlXlJSYl6yfSP8+bNU6WwjkI+t5TYSkAt7x2ZjDsqveuldNnR8yIXrcOHD6uScebFfjhLXiQfCQkJ6kFYmv84MjnvpY27XMd9fHx0qmOSvKSlpcHT0xP+/v5w5Fu35EXuhfIzMDDwnPJSxQ0I8HZHiL8ZzJl/L7+wBOnZxcgrOv/fj3QMnjJlChYsWPDveNaFhYWqhnL27Nl6K9dywYNIOVCkyrpJkyY6pfx27NiBpk2bntP82RIMfffdd6hevboqfbR25513qg4233zzjWovKe0ke/XqpYJI6wuPBJHDhw9XP08XRMrvyY1kwIABOsVxxcfHqzasziAuLg61a9fWS45Nmn3YNrdwVMyL/ZGHbqmJcYaSotTUVBV0OXpALOR+Kvlw9IBYWEZpkX1zrt79+wjuf+Wget+2fRA+v68hWoWd+989UzIDn8QQruiCl8PKWIvyBb/wwgvqwlQeMjC5DMkjvaLP9cleSgXvvvvukwJIcc0116i/L51mhBzU8nRh+29KvC3pZxLMOlKJ46lI/h25RMWWNGVwFs60X5gX+yPnirOcL850HXOm/XK+8nLvN3tw/8OZwA8XqdfmcU3Qesw27E+vmKEEnen6dTYueBApbRuleverr77CRRddpIK4/+qY8tFHH6kq54EDB2LFihWq/eSFfIqU6ms5mKXaQzRr1kxVG0h1ty0ZLL1OnTp6iYiIiCpHCd7/zgwg/26ul4UPsLAZ3l6zTy/ThVQhLUJl0G7pjPL888+rtjbXXnutaksgJXpSVSpVjNWqVVNtcST95ZdfVsHawoUL1fiMbdq00X/p7P3++++qR3hZ41P+/fffqnqgU6dOallKPnft2qWqwK1JYCnbdu/eXacQERFRZTiclQfklFHAlB6AXYeK9AJdSBXarUjGgZR5sWfNmqXGXJQBvW+88UYVVEq7RKnynjZtmgr0Fi9erHpPny/SzlEC1E8//VSnlJJhhmQw8apVq6J3794qTarfJWC0ncVGOuFIqaWUqBIREVHliQzwRVRzA/Awg0lrTeLQpI6nXqALyWV6ZwsJXJ999lk1F7YEitK+8euvv1ZDDklHGRn2x0J6V7/77ru47bbb0LVrV/z111+q95UMQD5hwgS9VdmkY430xpaB1B2ZtPWQjjXO0hnF0nPWGchYqvJg5AyYF/sjNUbSscYZOqNIW3xp5+4MnVGkk5Dsk/PRGaWyWfoNnOtweDPWHcEd9yQB6/SwgNXiget3w3i7tFDoQpP7pDS/Y8caO5KVlYW8PJsni/Ng7Nixqoe2/H0JEGXObBm+Rnp/WweQQob7mTp1qpqdRt7L2JXvvPPOfwaQREREVDFu7xSB9QvrY9g3a9D2o+V47ru0CgsgqZJKIqV9pIyzZNurybIsVd5S1d2lSxe1fCGkp6er6u0zeQqStpHSu/tMsSTSPrEk0j7ZS17mbo/DxsQ01ArwwaiWtRHuW/6SK5ZE2h+WRNqn81USWdlYElnBZNpDGdj70UcfxeOPP6460ciMMfJeqpql3aGUDFoP8n0hSJB3pgdveQJIInI8D/y8DdeOScUrl0RgzJX+aP/ELmxPSdNriYioLBUeRP7000/4448/VPWwFIJecsklqsONvJeBemX4HJlNRkaAJyK60F5fvRfvPOYN/NkSKDYfLI/UQOy7zdDnxRgUwXnGFiUiOt8qPIiUoXukHaIM+yOklE8GFRc1atRQY0q+/fbbZzQ/NRHRudqenGH+r75e0kp8kbTO2wwiXXsgYSKi06nwIFLaD4SGhuolqHEipZe0RaNGjVQp5N69e3UKEdGFU93fCwg4eWIBGFkoZgxJRHRKFR5EBgQEnDCI91NPPYWkpCRs27ZNLcsA5LKNjN9IRHShjW4ZAfSP0UtaZCwG3xgI/ypnP18/EZGzq/AgMioqSpVGypiNMq+2BI1Hjx5VPZqFTHH4/fffq8G/iYgutDbVg/Hig8Goed0eoLn56hKDqyYm4dObG5tr3Uo3IiKik1R4ECkdaWToG+mdLcGikAG9ZSaZvn37qk41UqUtLyKiivB8v0ZYNyMCG5aHY/sv4Zh7Y2tU93P8IWGIiC6kCg8ihQz0HR0djZYtW/67PH78eLi7u6Nz585qnusGDRqodUREFaGOnx/ah4WiRWgw3N0q5dJIZJcOZGRjXUIKdqVmoISdzchKpV0pGzdurKYftJDpBGXon6+++goRERE6lYiIiCrLpxsPo9X90ejcIxHNr4zDte9FIzk/X68lV8fHbSIiIjrJgj3HcNu4JGTPbgPsbQYsi8K3EwNxy2ccgo9KMYgkIiKik8zZGQv82Mp8ZxUqHK2Nn+YWweBA/GRiEElEREQnCfL2ANyL9JKVrEIziCRiEElERERl6F47FGgRq5c09xwEdzXM4IHhAzGIJCIiojLc2CYSl4xJA9ofArwzgPBkRLywAWvHycgqHEOVGEQSERHRKfx6e0f8MNcTL/weh7d/TsemsV3QJDRAryVXxyCSiIiIylQFbhjWuBbGXRyFBzo2RDU/L72GiEEkETmg+TuOwe3Wv+A2cBkixq7HvK0Jeg2R69qakIE6T6yBW/+lcL/9b7y15LCZyi4wdOEwiCQih/L+6iO48uGjwMxuwK+9ETulLa665wh+iU7UWxC5nnVx6ej4+G7ETW0BLO6Dkk+64eH7cvHkwr16C6Lzj0EkETmU136JBX6Thv3upQnwAP5qhecW7dfLRK7n400HUTi3GZBv1V5xZxO8/nWq+YalkXRhMIgkIgdioLBQeoV6li7+ywtbdpcxnh2Ri0gvKARyA/WShRuKd8htnkEkXRgMIonIgbihc0M/IDBNL2shqWjZ1FIySeR6etQJBRrE6SXNKx9oL/Nc81ZPFwaPLCJyKJOurA9022m+09OuuWcB/TZhwe1tSpeJXNCDnRsCffeZ78zzwaLfOsy8xzxfiC4QBpFE5FCiqgXgwHdt8L+ft6HVB8tw38L9KPquF+oE+uotiFxT9kfd8dzyw2jz0XJc+e1a7P+6HW7uWFuvJTr/GEQSkd1YeSgFTyzZgUmr92BrYrpOPVm9QH98OLAttt7VG+8MaA33fzvZELkuP3cPjL+4OTbf2QvfX90Z9YP99RqiC4NBJBFVKsvkaZ9sPohLXtiLyZdE4Jkh1XDRfUcwe8chvZaIiOyNSweRBw4cQI0aNTBp0iSdcpxhGJgxYwYaNmwIDw8PNGnSBLNnz9Zrieh88fGsgiWHUnH7c2nIn9kZKAkCUqsh85uWuH18CtYdtelEQ0REdsGlg8gHH3wQubm58Pb21inHTZ48GWPHjsUNN9yATz75BFdccQXuvfdevP7663oLIjovDGBvehawsZZOOK7wn2pIzJbepUREZG9cNoj88MMPsWLFCgQEBMDNzVKhVuro0aN46aWX8NBDD2H8+PG46aab8Nprr+G2227D+++/j+joaL0lEZ0z8/Sr6usJhJYRLHpmI7uwRC8QEZE9cckgcsmSJZgwYYKqns7Pz1dV19akGjs0NBTXX3+9Tin1yiuv4MiRI/jjjz90ChGdq6JiAz3rVEWTy5PMpYLSROGfhqhROegRGaITiIjInrhcECnV18888wxGjhyJgQMHIi8vT685bsOGDaoNZEjIiTcvKbFs06YN1q5dq1OI6FwVlhio7uuF126phRYP7ANaxgDNY9D1hf2YfU9D1A7g0D1ERPbI5YLIp556SpU+Pvfcc8jOztapJ9q9ezfCwsJUVbc1CSKDg4NVaeR/CQoK0u8cV5UqVdTLWbi7O88wMM60Xyx5Gd6kJv6a0hhbV1bH1lXVsfiRtuhU07FKIZ1lv8i54iznizNdx5xpvzhLXpzpWnw23AzbulwnNn/+fNx1111YuHAhOnXqhKSkJNSrV0+1e5RONBaRkZHo3bs3pk+fDh8fH50KFBQUYPjw4SoIXbx4sU492Zw5c/Dkk08iPDwcJSUl6iXB57x585CRkaG3sn/yuRMTE1GrVi313pHJA0BsbCwiIiIcPi9y0Tp8+LA6Tp0tLx5V3OCur8lFJQaKHSh7zrJfJB8JCQnqQdjLy0unOiY571NSUuDr63vCtfxs+HpWQVpeIbYkp8PL/I6q+3mjWdUAZOTpmZMuMMlLWloaPD094e/vf1IzLEcieZF7ofwMDAx0mLz4+flhypQpWLBggeqQK5+/sLAQrVu3dtnRW1wmiJTSwwEDBuDmm2/G448/rtLS09NRu3btfzvRWEhg2bNnTxVEysXHQoJHCSKLiopO2y5Sfk9uJPLvObr4+HjUrFlTLzm2uLg4tb+dgRzPEhA7A+bF/iQnJ6vmPM5QUpSamqqCrnMNiPem5+KJH/fiu/FmMBpsoG47A28/FYzhjWroLS48CbwkH+caENsDS02g7BtHN3jwYCxatEgvuRaXKIctLi5WgaLEyyNGjMDBgwfVS3pZy9OEXDAPHTqEzMxMtb08gcvTRVnxtQSQZ3JhdaQSx1OR0hRHL+myJseBs3Cm/cK82B85V5zlfDkf17GMgkKM/mA3vnu8OhDTGFjfBIdmNMF1rx7EuriKG8fUmfaLs+TFma5fZ8MlgsicnBzs2bNHdaLp0aOHqsqW1+WXX656Yc+cOROdO3dW1dyiW7duqtRKqg6sSVAp6dK5hoiIXMOhzBz8M88XiDeDyH+5Ie/LZvgp+pheJnI9LhFESpW0tHv84IMP8Pnnn+Orr77C3Llz8e6776oqbRlIXNoxSjtIIVXZ0rlG2gNak9JKSe/YsaNOISIiZyftcz0CThxPWHEvRFqWy3QrIDqJSwSRMm3hRRddhMsuuwyXXHKJevXt2xeXXnqpGvJHhvPp06eP6kAiZOgfaTD76quvqmWLxx57DC1atEDXrl11ChERObt6QX6o11qGgyssTbDoFIfWtfz0ApHrcYkg8lSkmlteWVlZOqWUzKf96aefqhltJMCUqQ+ls83WrVtVYNmgQQO9JRERObtQby+8/WB1hN25HfDJALwzgeGbMfZpD9zeoa7eisj1uHQQKUMLTJw4UZVC2hoyZIiq8paOONIbbvTo0fjyyy9VLywiInItgxvUxN+Tm+CVpccw/s84/PxGLbzev4VeS+SaXGqcyLMlPbKlSvxMyRA/Mi6kzIrjyKTXmQzx4yzD4ljG8HMG0j63bl3nKAFhXuyPjBMpQ/w4+jiRQkbfkGFknGFYHBmuSPaJMwyLYxnBxNEn5pD75NChQznED51aeQJIIlexOSEdtR9fA7f+S+F5x9+YuvS/Z3IiIiLnwSCSiMptbVwaOozdg6NvtwQW90HRjG546L5sPLNor96CiIicHYNIIiq3DzceRMk3UUC+VbXajqZ4dU6KXiAiImfHIJKIyi0jv8AMIAP1koUbirfpt0RE5PQYRBJRufWIqArUjdVLmnce0MEMLomIyCUwiCSicnuoSyOgn7R/tBpjte86fH5vQ71ARETOjkEkEZ2VrI974Nllh9Hmo2W4+ru12D+nPUa3L531iYiInB+DSCI6K/4eHpjQqzk239kb317VGfWDHH/sOiIiOnMMIomIiIio3BhEEhEREVG5MYgkIiIionJjEElERERE5cYgkoiIiOxeXkkRRs/eDre+S+F21Upc8+EuZBUX6rVUGRhEEhERkV1LzM7HwGnb8OVzQcDSPsC8nvjm0eroM2ULMgoYSFYWBpFERERk1zYlpWPZlwHAwUidYsqqivVzQ7HiSJJOoIrGIJKIiMrNMP/bkpSGjUmpOJyVrVOJLoyjmflAehlj0e73wbGUYr1AFY1BJBERlUtiTj7u/m4n2g6KQ4c+CWh/x2G88Ns+vZbo/GtbPQghbVP1kpVOiQgL9tALVNEYRBIRUbn876tofPSUP7CuBbC9GZLnRGH8xEwsiD6mtyA6v9pWD8alwwqBWgd0iqnVdgweaWBYk5o6gSoag0giIioHA/N/ygGi6+llbUVbvL/mkF4gOv/mjm6LOYs90e3Tler15dfBWHh7O72WKgODSCIiOmMl5n++gWVVHxbjWBrbprmChOx8PL98Fyas3I2fYuJ1asW4JqoOVt/SU71GtYzQqVRZGEQSEdEZqwJ3tGtpBpHe6TpFq38YvZsE6QVyVqtiU9Br2gZMGFwdzw8Jx+U35eDG7zbrteRqGEQSEVG5fH1fI9S5LwaokQJ4ZQC9otHj6XhMuayF3oKckQz2ffnL+7D7qQ5AdlUgw3ytbojPX/LF1DX79VbkShhEEhFRudQN8MfaF1vgg1/T8dwfcfjuwwD8dWc3vZacVXx2HlJ2+ZjvvEsTLDbWx/a4HL1AroRBJBERlVutAF/c1bYBxl8chauiaulUcmYB3u7wDjH0khX/bCTl5usFciUuGUTGxcVh586d2LNnD7KysnTqyYqLi7F//37s2LEDBw4cgGGUcfIQVbK1cWkIH/sP3Povhe9d/+C9FbF6DVGp/JIi3PPtLrj1WQK3K1di0NvbkVlUoNcSnZkwLx9cOdjTfGM9lFMxMHAvHulp01ufXILLBZGTJk1C//790alTJ3Tu3BnXXHMNfvnlF732uKSkJDz66KPo1q0bOnTogB49euCxxx5DcnKy3oKo8v19JBVdHtqDpHdaA4v7IO+jLrjv3kyM/53tk6hUal4Bhr+/Ax887QMs6wvM74lfHo9At8mbkZLLQJLKww0TrorAgKdTgE4xQFQ0avxvOz56ujp6RlbT25Arcakg8q233sJrr72GkSNHYuvWrVi1ahWqVKmCUaNGITb2xNKbcePGYfr06Zg1axaio6MxdepUvPvuu5g4caLegqjyTVtnBovftQIK/HSKG7CtKSZ8naCXydXtTs3Er197A9H1dYopPxg75obj1wOJOoHozDQOCcAPY5pi+2/h2LgiDOunNMadHerqteRqXCaI3Lt3Lz7++GNccsklGD9+PBo2bIiWLVuqNHn/wgsv6C2BtWvXqoDxq6++woABAxAZGakCz9mzZ6vtV6xYobckqhxmqKhkFBYBJZYA0qIKiraz6QWVilVzDtseI6b9/jiabB4/ROXkXcUdLUKD0S4sFHX8yzi2yGW4TBAZGhqKJ598UlVRW/Py8kJgYCDi448PmPr999+jadOm6mVt8ODB8Pb2VkEmUWWyhIg964QCNY/qJc0nF2jH4IBKtQ4PRFibTL1kpfMx1OCcw0R0DlwmiKxatSpuvPFGdO3aVaeUWrNmDdavX48rrrhCp0BVdTdp0gTVq1fXKaWk6jsqKgqrV6/WKafm6emp3zkuNzc39XIWzpQXiyd6NAH6RJvvzMBRMcPL/uvx3f3N9DK5uqahgRh+pfmmwb7SBNFsD3pfnY/RrevohBM527nvLJxpvzhLXiQucGVuhgt2Oc7MzMS3336LL774An/99RfuueceTJkyRa8F6tevrzrSzJgxA76+vjoVyM/Px7Bhw1Sv7T/++EOnnuyzzz5TbSyl5FJ+R75iDw8PtGvXDkVFjlNCVFJSgmPHjqFOnTrqvSOTi9Xhw4dRt25dh8mLp7sb3D3dzXfmKVpsIK+w9HPLRUtGC5Dj1LOKgcTcArzyVzR+2pOIFtUDMOWSFmgYFoi8PPs/1qzz4ujHmL3mpYp5n/bycMO3u+IwaWUMikvccEe7SDzQvRkK8vNQYnMHkHxIzUxISIiqqXFkct5LJ0l/f3/4+Mj4ho5L8pKamqoKKAICAhx6tBDJS3p6uvoZFBTkMHlxd3fHwYMHkZiYqM4TeRUWFmLy5MmYP3++3sq1uGQQKRd6CRrlIJZSR6m2fvbZZ9GqVSu1XgKNXr16qY411heegoICDB8+XAWGixcv1qknk+B03rx5aNu2rQoa5Ybi5+eHMWPGIDfXUmJk/+RzJyQkoHbt2g5/g5eL1ZEjR1T7VkfIS4iPB7Yey8S09fsRZL7vXDMY17eNQHJmobpwHTp06N+A2MOMEmT8Nnd384nYXM7ML0aBGXQ6Atu8ODJ7zouU9/h6VTFf8lBiPhCbDyRZ5nFSFsmHPDwGBwc7RRApI2rI9dcZgsi0tDRVIOEMQWRGRoZ670hBpJwPMprLxo0bVTAv+ZAgUjrfzp07V2/lWlwyiJSSRHnJQSAHw80336wumEuXLlUnqNwEevbsWWZJpASREhieriRSgs+aNWti6NChOsVxHT16FLVqOcdAwlI6LKWqjuCPA8m464to7HvefLAJLYRbq1Q8+WIBJvWOUuulVFUCYmfAvNgfKb2Tkki5Hjq6lJQUVRIp7dkdnRR8SCBjfV9yVJYxmiUgdnRS67ho0SK95FpcsjJfiqTlRJSnCBkD8sEHH8S+ffv+LY6W6qicnBz1hGFN4u28vDz15PRfHKnE8VSkNMWZnjEcpaQrNisHw8cfxL5nO5sf2rzAJofCWNYQL48vwudbS4eicqb9wrzYHzlXHL1k2EL2CfeL/XGWvDjL/jhbLhNESgnBtGnTThoPUsgTtwSWloNB2i5KCZw89VmTC5EMFdSiRQudQnT+Hc7MRc6OQPNdadXjv/6uh5hEx384ISIi5+AyQWRMTIwaQPzTTz/VKcdt27ZNBYjS9k/IjDabNm06YdgfIdMfSrs6mcWG6EIJ9vGEZ3AZ7dX8M5Gaf2LpOBERUWVxmSCyb9++qo2ilEb+9ttvqpRRXtLu8b333sOgQYNUO0gxZMgQFSjedNNNqhOONACWHlkjRozA1VdfjT59+qjtiC6ERsH+6D/EDCKDrKfYLILfVbG4uV3pgw4REVFlc6k2ka+++iq6d++upjmUmWskGHz88cdx+eWX4+2339ZbQTUml2kOZYByGVdSgsr27dujXr16qjTTGRoCk/3yquKOidfUQb+nE4BWMUDzGNR5YCu+GhuJDrWC9VZERESVy+V6Z2dnZ6thfbZs2aLaQV500UVo3Lhxmb0QZUwumV9bqsJl8HEpnZRBy/+L9M6W3t4yVaIjkzaiUqVvqeZ3dI7Wcza3uAgx6VkoNk/RGj4+qOV/vEemZSgZZ8C82B8Z2ssZxokUMsSPM4wTKeSeJPtE8uPorIf4cWRyn5RaTvbOdhFy8kkw+L///Q+33367moHmVMNYSEmklELK+I7Shf9MAkii88XX3QOtq4agXbXQEwJIIiJXcCgjB+sSUrAjNR1FKHtcU6pcLhdEEhERkX37elssWo/Zjc49EtFy2FGMnBaDeCcYOs/ZMIgkIiIiu/FLTCJGjT+GjJltgL3NgJVRmD8xGLd8GmOude1xGe0Ng0giIiKyG99FxwHftDTfWY2Vm1ATv84tQXZJkU4ge8AgkoiIHN7MzYfx1NIdmL75ILKKOJ6qIwv0NINHnzLaQGYVoZgFkXaFQSQRETm0yz9fh1v/l4dXLo3Andd4os0zW5FelK/XkqPpWjsUaHVEL2lueQjsVgQvd4Yt9oR7g4iIHNZDv27HTw/XBNY0AYqCgD21sX9aY7QZt0lvQY7m2hZ1MPyhLKDTIcAnHQhNRe1xa7FyXHP4uJU9mgpVDgaRRETksDYnmkFGUoRe0nKDcGi9fk8Oaf7o9vjpay+88PtRvPlbCjaO7YI2YY49pqQzYhBJREQOq6a/t/n/MtpAFmTpN+SY3DCkUU2M6xmFhzo1QnW1n8neMIgkIpfy485jcLt9FdwGLEPtR9bjm80Jeg05ovs61wc67tBLWpP9uOl2zjNPdKExiCQilzFjbSyGPxwHfNIF+K03jr7ZFtfcE4sFu47pLcjR9Iyohtsf90K1K6OBprtRpf9u3Dg+C9NHNdVbENGFwiCSiFzG5F+PAL+2Mt9ZGuebP1e3xHM/HdTL5IimX9McG2bXxvqV1bHru9qYdV0reLpZjTFIRBcEg0gichEGCgvdzJ+epYv/8sKW3RzA2NHV9fdHh/BQNAkONJdkP5Or252aifWJKdiXwfaxFwqDSCJyEW7o3NAPCEzVy1pIGlo2Y9BB5CxKzAfG536PRtToA+jUMxEtRx/BXV9F67V0PjGIJCKXMWl4A6D7LvOdLnmskg303YgFd7QtXSYihzdpyX5MfMo8x39uDexphryfovDReDOw/G2v3oLOFwaRROQyGoX44+A3bXDPL9vR6oNluGfhXuR/fzHqh/jpLYjI0X2y6hiwvrle0nY1xdSFHInhfGMQSXQamQVFeGV1DMat2IVvd8fpVHJkdYP88d6Atth6V2+8N7ANvP7tZEN0/szeekTN5f3hxgNILyzQqVQRwvzLPqczU9n2+XxjEEl0CtEp2ej3wXo8dXUAXhxUAyNHF6LT1DV6LRFR2a6duxE33ZOt5vK+e4Q32j61HfG5OXotXWg9GgYBVY/qJS0kEV06+uoFOl8YRBKdQr/XtmPdY82BozWB7FBgfT2sf7U2Hv3DZmBjIiLt6cW7MfeRasBfzUrn8t5XCwffaYxOL27TW9CF9tawZmg05hDQ5BjglQ60jEXTZ3bjnzGd9BZ0vjCIJCqTgSPSBrvAZq7WoxFYd4DDRRBR2bYmpQGxdfWSlh+I2HW83VakDU90wBc/FODZ349i5tcl2DG2h15D5xOPaqIyuSEwWE4Po3TxXwWIz8rX74ns0zOLd6HJu0tw2RersTXZDGqowpTO5Z1XumCt2P4fPrOLCzBszlq0/GAp7v91C4rN/xxVkLcnrm8eiQm9onBzq0i4uzHcuRD4rRKdwu2DQ4B6h/SSMAPK7jsxeXATvUxkX1JyC9B68j+YNNofMff3xe83dEebfkcwcQmHNqkod3aoC/TcrZe0Rgdw3S3V9YJ9+nVPEgJuXYsF17XCjnv64N2BjeAx6G/EZrItJ50ag0iiUxg3tC6ueCIHbr3MG3CzPah6w3Y8Oc4Xw5rW1FsQ2ZdZW45g22fm8RkfqVNMW5rj5U8zkVxQRukYnXddalXF/Y96I3zEHvO6YQaTvaMxakImZoy277m8H5t3AJgj46VaOp/4A8tb4+avd+plopMxiCQ6hWBPL8y9uyl2LwjH+hXh2PheA7x8mX3fCMi17UnLAnbaPuS4I2edL3ILS/QyXWjThkdh/cw65nWjOnbPr4EvRrWCn4c9DyVl4EhCEVAQoJe1nCBs2F6oF4hOxiCS6DQ83dzRJChIzclbN9B8Mqf/lJibj7UJKdiSnIasIt6AKlKHGsFAc9sBlQ2gYSrcnGg+6bziYqw5loLN5jEWn5urU+1LpJ7Lu2lIkAN8925oW88X8M7Wy5pfFnzDeQ7TqTGIJKLz5p+jKbhownZ06ZaItpfFY8D4vdiYwI4dFeXq5rUQ0l8Gxbfq/NV2F24fHYo6/s4xRt7OpEyM+HQrunZNRLtL4tHlgQP4ef8xvZbO1tjLapvHinXbWTN47LoDn11rM/MLkRWXCyILCwvx+uuvY8SIERg+fDheffVVZGZm6rUn2rdvH+677z4MGjQIDz74IGJjY/UaIrK1LSETV0/Zh+hXzZvO/mbAhiiserUORr+3D0ez2R6vIoR6e2Hho03RafweYMgKYMRqvPiGFz4a5RydwVJy83HjR3ux8Kk6wEHzGNsUhcMzonDtGwewKT5Db0VnY2hUON56LRTV798AXLYctR/ZjO/frYdLGofpLYhO5lJB5ObNm1G9enXMmDEDJSUl8PLywsyZM1GrVi2sXr1ab1Xqyy+/RIcOHbB161aEhoZi3bp1iIqKwpw5c/QWRGTtr9hkxH4ZCZRYlXgVBGLn19WwI4k3+IrSo24o1j7XGsZPF8P4pjue79/IvNA7x6U+JiMb67/3B5LCdYpwQ+YXTfDrPs6LfK7G9IrEsWkdYPzaC7FvdMKVzWvoNURlc5kgMjc3F0888QQaN26MJUuW4Pvvv8c333yDX375BW3atFEljRYpKSl47rnnMGTIECxfvlwFlKtWrUK/fv0wefJkHDlyRG9JRBae7m6Av+24mqbCAuS54NTBG46m44nFOzBp1R6sOZqqU+lcFBUbqOJfxm2rShEystlxyFGVGAbeXbcfzy7bic+3HYZx0vi8ZK9cJojcsGED/v77b1x55ZWoWfN478V69eph1KhRSEpKUoGi+PXXX5GcnIwxY8aoZYs33ngDGzduxJo1nD+ZyFarsCD4tk/SS8e5dc1ArUAZgNn5WbpPfLn9MPpN2oXJl0TgmaHV0PvuY3h3A8dqPFeNQvwQ2UbGLSwqTbDoEocWNdjxzdHIg2d2UTH6T1+H+29yw0sDauPGUW5oPmGd3oLsncsEke3bt8dff/11UmAo8vNLG6FXqVL6dcyfPx+tW7dGRESEWraIjIxU6VKS+V98fR2/Ebt8H25uztOj07J/nYE97pcutUPx7MPe8B4Yo3p1wjsHoY/8ja+er40ONYP1VidzpmPMx8sdGxIyceO4ZKS/0xUwgoDUasj7MQr3T8zCskMpekv7JueKPZ4vNfx88daYcITdsdP8srPNC202qozYjHHP+GN0mzp6qxPJ8eUsx5i97pezIfnw9ffCiM+2YenY+sBO85VvXie2RWD3Gw0w4KONekv75iz742y5GSb93iVlZGTgiiuuQFpaGtavX68uNp06dULDhg1Ve0k/Pz+9ZWmwOXjwYHh4eKjSylP54osvMG/ePLRt2xZFRUWq/aX8HQlgpVrdUcjnTkhIQO3atdV7R+DrWQV+Ph7mzdtAQWEJMvNLp+2S/SrNEORBwFHycipy0Tp06BDq1q17znmpYt5bg83vq4qHeSEsLv2+CorP7pIgt2kv8+/8eSABS81gqYqbgSsa10bPeqFIybEpOdLOZ14qm7uZl2NxR7Aq3we3XWdeN6JtgpraCfjg2zTc3Coc2QX2m1fZJ8eOHUNwcLBqN25P5BjzcHfDjqRMfLsrDkXmed6tZlVc17YOkjNPbjMh573UKsn118fHR6c6JsmL3Kfk/hMQEGBe4hz31i15yTTvvX4+VdD+3SOInXjyvNYhY/5G6utRSE63n6kX5XyQJnBSI+np6anyIZ11o6OjMXfuXL2Va3H5IFLaSb722mv49ttvcdVVV6k0qeLu2bMnpk+ffkKJYkFBAS6//HIVGP7555869WSfffaZ6sktAacEnvIVy4nfrl079buOQm7qcjOpU6eO3d/gJRjy8vbCz7tjcduPW1Ez0As3tqmNR3q0QEF+Hgzz9nP48GGnCFbkJn/gwAHUr1//nPLiI4GjGW/f9v1m/L4/CR1qB+H1y6LQpFow8vLO7jiVm7y3+rvyzjyGzED+dEHp+cqLPZAgMj72MLYZfhh8XT6wtr5eozXYh2lfGri/SyTy7DyIjI+PR0hIiN0FkUKOLKkGrWI+MCrm8ZV3ioHU5SYvTZX8/f2dIohMTU1VwYszBJEZGekI8fNA9w/2Yf2j7c1U99KVirk/71oG44Ne5rXIfsapdHd3x8GDB5GYmKjOE3lJECl9JaQG0yVJEOmqbrvtNsMMEo233npLp5SKjIw0Ro8ebeTm5uqUUmZAaAwcONDo16+fTinbxx9/bMybN08vOS7zpm7ExcXpJftWbL7u/m6ngd4bzCurXF3NV/BRo+t7/5RuYDKDSP3O8ZkXMv3u7B3NyjP8xqw0v6dE/Z0VGui+wfhqy1G9RcU4H3mxF3FHDhupBUVGuxc3ms8tWcePRc8so+7j64x9qdl6S/uWkJBgmA/NesmxmUHkSddyR2UGkUZ2tmMcQ/8lIyPDMAqyjU/WxhpoYV67LeeKvFrvNCYt3qe3tH+DBg3S71yPS1bmS+/rO+64QxU/T5ky5aR2kvLUKk8XtiUj5vel0qVU8b/Ido5O8isvRyBDyHw8qwhYJk+0WnpN/PNVKObuLB3f01HyUlEmrYxGzuym5vdkGQfOPK7XNsfdHx3Sy1RehcUlCPF0x+Qba6PDY4eBljFA8xi0fnYPvnigPhqEHG8eY88c6dx3Jc60XyQfWXnFuLVTbVz/hAF/aUvddA/8hu3E3eNL8FTfBnpL++boNSjnyuWCSPMpTlVbz5o1C5988gnuvvtuvea4Zs2aqbYnZbVfzMnJUdW7ZF/2pGahOCZIL1lZH45DiZy2qywxadnmE5X1eHumIh+kr7OuVqKzcWmD6vhzQkNsXlYNm1ZUw7LHW6JnRDW9loiEDO0jPr8pClvn1sD6leHYOjsS71/RQqWT/XOpIFIaWEuAKG1k1q5di5EjR+o1J5LxIHft2qXaPViTwFKGCerevbtOIXvRMjwAwc1k6A8bzePh6dhNoS6YLrVCgFCbIXk8C4DILL1A5yLEywttqoWirfkK9bG/toWVy8DW5DRsTErFoSyb+Zqd2LGcPKzT88rnFpe2O96eko4Niak4kOm6553MLd4gMFDNNd4wKECnkiNwmSAyLy8P99xzj+px+OOPP6qe06ciHWIkYJRBxq3JdInS6eaiiy7SKWQvGocEoP/gYqCGzBusVU1Ak2GZuLF1bZ1A1u7pXBfouc98Z9WJpv0uvHCbmU50gSTn5uPu73ehzeA4dOidgPa3H8Yzv8Totc5rdVwyur2wA527y7zyxzD8jRjct2A7Wl11BB3N76HtLUfw8LxovTWRY3CZIFK65S9dulT1lpY2kAMGDMBll12mXpdccgkGDhyIFStWqG1lVhsJON988021rQSTMof2hx9+iBtuuAEtWrCo3d64m4fy29c0xP+mZAPDVwGXr0T/cUex9qm2qOrLUqCy1PD1xZyJddH8qe3AwGXwvG0N3n4zGOMGOkZbJHJM//sqGh8+7QesMa+jO5ohZW4UJo3Pwg974vUWzmdTfDquen0/Drxu5nmfzCvfDL8vzsd7L5rXpmUtgZ3NkPF9FN4an48ZGw7r3yKyfy4TRMoYgVL6KAGgDLMjXfOlu771S4YdsHjllVcwdepUNTuNvJcxJN955x1MmDBBb0H2pk6gLz68vgmM+T1g/NgTfzzQFsGeDCBP55o2NbFjUlsYP/dGwYwueKBHPb2G6ML4fqH5oLfb5jhb3Q7T/nbeDl0rYpMR/6Xk2aptTe0cYH0TvaBtaoW3lnJaXXIcLhNE3n///fj9999VVfbPP/98wksGDl+4cKEaG9LabbfdhtWrV6sxIaUt5E033aTXUEVLyy/EpL/2YNyKXfh+j1WVNZEDSc4pwPgVe/Diyt34IfqoTnUlBnwDy+q4VYKEVPsZVPp886xi3mr9bXrx5pc9yscxB/0eio0SvCPzXy/fic+3SyDsfL2W5+06iqeW7sCUNTGIy3aciUMuJJcJIs9FeLhND1aqUNsTM9D3vfV45spgvDioJq6+oQC93+fcquRYNsSnofe76/HCsKoYN7g6rrgxD8NmbdBrXYUbOrT0AnzT9bIWeRh9mpUxuoKTaBMWBK/2CXpJOxII1LaZBjM8Fv1amekORh7y+3+8Dg+MdtfzXxtoPnG9XuscnlmyE1c9nIhXLonA2OHB6PjYHqxJSFW1mq6MQSTZvUtf241Nj7cCEmsA2SFqJpDlk8Px7JJdegsie2dg4Csx2P5EO/OOGwZkhgL/NMCCV4LVeJ2uZO59jVHnXjPPNc0AyisD6BmDzk/H4u2BLfUWzqdHZFU8+ZAn3PvFAD5mnj2zUL1zOhrcvheom1T6PXQ+gJbP7MfX156606e9umrGViwb2xDYUxfICwa2RmLXG/Uw9JNNegvH9uH6g5j0hBvwSxug2HzYiQ9H/PtRGPTiAaQW5MNDpkxzUQwiya4VohhHY8wTtMhm2IcD9bDhEIeiIceQYt5oEvfInO7Hp1FVdtbDltgyhqZyYrX9/LDuxVb46Jd0PPdHHL752A9r7j557mRn82LPKPw5MwQT/jyKScvjsOKpltj6fHt8ujAbz/4eh69memDbmBObVDmKHYfzgSzLpAVaWnWs3WWmO4HodPNes8m2vbg3Utb6Ia+oGFbdKVwOg0iya57mIeofLIepzSwNbrmIzy7QC2TvtiVmoPn7S9HlkxV46a89OtV1+Hl5wDdE7jQ2x7FXLhJyzuxGeyA9W31/HaavwLPLHLsUvqa/D+5s2wDjL47CiKjjQ3Dd8uNmNH13CW5esBFJ+c7X5qx3ZBie7dEMT3VriqbVAuDv4YFbWtXDhF5RuK5FhN7K8dQI8jT/b9sGsgQJZUzY4QhKzP+u+24Dmr+3FA//sRVGFTNQDCvrfpOFwmLXntmJQSTZOTfcPCgQiCidurCUebHqvQsvXdZIL5M9e+HXvWh96y7surcP1t5+MZ7tXw3Vn12p17oGH3jgusE+ZvRk3ZnGPI4vicYzff57SKWpKw6hwa1b1fe38c6LzWO/JtzuXG6ucY4b2P60HLjdtQKfjaqL6Pv7Ytaw5gi/bBt+izlxwgeyT/f0qaGm9zxBm914baTjDRe2ITYD7revwpzrGmPXfX3w1qVNMGVqHox+u/UWWq2juORGb/OByBvFJa4bSDKIJLs37vK6GPZkJnDRXqDZHlS7eQfGvxCIQY3NCxfZtbTCAkyenQEs7KRTTPnVkDi/Lt74x/kHmLY2/opIDHkqHehq5rtZNMJv24Ypz4aif4P/6rhn4LnPE4B5HfWyqSAE+LkpHl+8Uyc4tucX7wE+bwXkhOoUM+D+uxVu+kgGwyd7d3f3SIx6ohh+A8xjW+a/vmIX7h1v4NFejjdk2NO/mPeZL9sARZaOXuax+Gdr8wEwA63uMte1MI/V9jEYOvEYZt7WGF5VPODCMSSDSLJ/4b7e+Pbepti1MBwbVoRj4zsN8Vyfxnot2bN9qTnIOyjtAG0uNdtrIDrWtZojRAT44fv7m2LnL+ZxvDIMG6Y2xsPd/7uk5lhuHjJjZVgcqTK0ElsT2/Y7R5uzGPM4OR5AagW+OOZqndcd2Bc3N8PWb2qWzn/9WQTeHe6Ik3IY2J+cC+TZjBSQaV7DYgOw9YN62LgsHNv+DMP3t7RBHX8flJQ431BG5cEgkhyCp5s7mgUHoX14KCLNm7GjyCsuxppjKdicnIb4HNcbV6xJNT/UbFpovrMZ+65JPLx9z//j+4GMbDU38a7UDPNftL+Lu1cVd0SFBKN9WKgKKs+EzCxUt6GbebW2CbprJMAn0DluYF1qmzdt3zS9pHmZAXId15lX29G5meFEw8AAB5//2g2dIgIBn0y9rPnkwL2GPLB5oJ157rYMDSkd+5MYRBJdKLuSM3HNzK3o2jUR7S6JR+f7D2DRPued2q0sge5eGDnEB2hgNRuJXxoCLovHExc31Annx8xNh9H6/mh07pGI5lfG4dr3opGUn6fXOrY7Lw8Bmh7USybvLKDPPrwxIEonOLaHL2oAdJOhjqweNjrtxJu3s8aBKtbDfSLNY0+ORctDrnlMdt6JmTc31ctkzX2cSb+n82TDhg3w8fFBy5aOPe6ZYRjIyspCYKDjDX5bloyMDAQHB+ulCyslrwBXvbsHSyfWAeLqAvFhyNgUhgXFOzCwQyBqBVhNf3YW0tPTKywv56prg0C4Nc7AXyW7gPoH0OGGbCx5qgXqBpaWxJ2PvPwUfQzXPnMMBXPbAqnhwMEw7NxYgB0hR3B9p4prO3uh9kun+gHwbJyF5e57gNr70eLaTPz8TBO0CLswA3RnZ2era5hMB1sRQry9UM+8XG4L2Y/UgD0IvDQB7z1dA/d2N2/o5yg3NxdeXl7w8Ch7hhhHkpeXp/aJ5MfR5eeXNsXw9vZWP+1F7UAf1Gxegi1BMcgIika1QUn4+JnauKH98VEErMl98ssvv8To0aN1imtxM78AF24SemFMnz5d3UhGjhypUxyTtPWIj49H7dplnzyO5vDhw4iMPPeb0plYeywFXYYkAettnl6DU/HywmQ8edG5lbAcOnQIdeuawakTOB95uenHDZg9vLX5zqbdYL9NKPqzNdzN/yqCs+yXhIQEhISEOEWwUpiVBk9/f/NuZ3NsOKDU1FS1T/wlPw5OHupFUNCFeRCqOAauHHQZ5v38u152LazOJroAikoMuAeUcXpVKUR6duW0Y8stKsaUf/bh+eW7MGenzG3rPIK8PQCPIr1kJavQvMSf3+fkxJwCjFuxG+P/2o0fXXL+a8fxc0wiHl2+FxNWxqj2snRcfFaeGm90gnkcL4w5plOpvLYlZGJN7S54c+MRrDySrFNdB4NIogugUYg/ItrITCQ2gU2XOLSoWfEdg45k5qLfh+sw9hofTBhYE9eNNtD61X/0WsfXrU5VoIX1WKIm9xwEdyuBx3kshVwbl4o+76zHi0Oq4YVB1TH8xjxc/eVGvZbsydR1ezH4scN4e3hTPH9FdXR+eC8W7XetNsmnsvJwMnpN24iXBtbA80PCMfTmLNw2f4teS2fq211x6Dd5J+K+ehGP9PdFvzuS8MZa15rGlEEk0QVQ3dcHbz0Qjqq3bQe8MgFv83XVJjz7lDdubFPxM1Nc9vY2/P1YM+BQbSA3BNgYiW2v18Xt85zjxnFDqwhcNiYdaH/I/K7Nn2EpiBi3Af+8IMOMnJ85yQyUYNAre7FD5r/OPD7/9feTgjB59V69FdmDb3YcxUNPZQPzO5jPcYFASjUkfdISI1+Mwz6Zws6FZRUV4vKXDyD6afO7yTOP4XTzAWxVI3z6kjfeXXtAb0X/ZXNCOkaNO4bEN7qa11QPILUaCn9thkcn5OLnvQl6K+fHIJLoArmiSS38/XojTFp6FBMWx+HXyXUwoXdzvbZi7dlfXBo8WkuqhTUxzjNv88+3dsCPcz3xwu9H8fYvadj4SBc0q3r+OoUl5OUjeY+0EbSZ/3p7XWyNZVWpPdmdZj60rbdtm+qOnDXBSM8vo9mDgwgN8IS//7m17TyanYe0XXIM23RoWV8PO+Mr7noQZOYl6BzzUpkOZOSgaGs1vWRldS0cSXOO8VvPBINIuiAWxsSj4bTF6D7zL3y6xWpoEjv34vI9aPLuEvSevQrrjqXo1LPXJDQAT3VvqubLvazRf81McuGEB0uVrm1bzGLE5zrPxa6Kmxsub1wL4y6OwgMdGyLM7/x2CvH3dIdPcBntK31ykZRTOQOnS+noqO83IOq9pbhj4SZkFlf2AO4Gbpq/EU3fW4JbftqIlILKGWIpzNcMTkLK+Lfds5FfdH7bJCfn5+OyL/5Gm4+W4ZE/tpkpF6av6nvrDqDBe6vR/ZO/8euBsy/pCvTygHdIGZ8xIBvJeRVz/Hy5LRb1p61Et5lr8c1um2YoF9C83UfVfamHeV+avc1q2LGzEOrjCbfQMh5IfLOQWSBj47oI6Z1N59fHH39szJ07Vy85ruLiYiM2NlYvnZn8oiLjlq+3G+i2ybxKSc9/81U11ujz0Vq9ReU5dOiQfney1JwCo/vbawzU2X/8c7fYbjy2aLfewr4cPHhQvzsz437Za6CR+bLkTV4dthizNh3WW1Se8ualMt00c5eBGrFW32ORgcvXG4sPJKr1FZmXDXHpBm5bYcDT/Kk+S46BfquNtbGpeouzd+zYMSM/P18vnZk9SVkG7lxuwCdVf55cA73/MRbvK/1uKtL+tGwj/MG15meQCen0vqqaYHSetMlIyytfvk7n601HDYz6y/z7BaX/hnuGeTwsNXKKC/UW5y4zv9AYMmODgWbmsWfJS/1o46Y5W/QW5VVsjPx4h4Fq8cf/nhzH164zVh5K1ttcGLmFRcbI2ZsNtN92/N+uecAY9tlGvcWFkWfel278cquBLua/bfl3ww4bl05fp7coPzmOur5k3ue8Mo//zSrZRq2xa41dyZl6K+fHcSIvAFceJ3JDQjrum5AJLJHhVrTcQBzIykSHHoVoVq3yxpw83TiRs7cdwfvjvYE9VgNgJ4ZhfXEsbhwYhBAv+6p2Ke94hD0aBWGXXwJistNR7JmE4P7xuPchdzx+cSO9ReVxpDEv2zf0Q3TAMUQnpwNByag+PA4vPxSKa1uWDoNVkXm57ZsdiJkcBeRb/j3zGD0agr+Cd+O+i+votLNzNuNE3rdgB7ZPbGbVbMIDiA/Fnz678Ej/im0HHOLjiVp1S7A+5yjSi9KAamm49JlEfHhjI0To8UnPh0Fv70DG9LZmrKqrhg3zZ1wIopvuxsiWtUrTztGivccwYYIZo2wwv1uLtKrYlp+IIf08UTvApnnFf3JDm/q+iA48hr2J5nEckoyaV8fi7YfDMKxpTb3NhbH8cDKemJAPrLKaEjErBLtzUtGrN9Ag+MIMXbT2aBrGTMgGlrXSKaacIOzLzkCXnkWqxqi8fDzc0bieB3b7HcMRuR6Ep6LZHXH49L666FTTZgpPJ8bqbDqvYlLME3WvTds7sS4MsSn2W8QfnWZ+7h22F1A35K8LQHaezZR9DsjLzR1f39EMO+bVUHPbbppeH1OGVE77TEdWP8gP3z/QFDt+k3nczYeMtxrjga719FrA2/38dOL5bwYOyBy/uTYBa14Admw+9+pabw83eHmU7/ZQOv+1zbmf74cjldR5/YaWEVj7QQMs/cEDa/70x4I72qL5eX2ILUHsUfO7LrQJ4sygaMOu89dMJCbVvDbtCtNLxxWvC0HaWQ4X1qxqAOY/1ATb/gzHRjmO32iKW9te+DF0VV72VNVLVjaE4ljahWurukf+3eiy7kvVcDT17P/dPnXD8PMz9dC9xTPYt6kBVj7bwkyrvGZLlYFBJJ1XLasHILCZzbyjovkxeNrxuMXta5g34xaJesnCfPpvmAwz/nIK7m5V0CgoUM1tWz/w9E/8CTl5ag7qLclpyC6q3OC/sKQEGxJSsSkpFbHZld8RyLuKO5qXMf91dHo21qVk4kCFfEY3dIw0AyKf0gGb/+WTC7ca5zZHe2x2HtYkZmBTYhoKjTN/gOoSIfNfp+slzdcMpiJzEFeQpY6lhNyKnT++urc3OlQNQsewEDPAP93tzsC25HRsSEzFwSwz4DgjVdC6gTfgabO//TPgG3r+HjzbVA+EZ/NUvWSlZSoK3YqwIzUdm5NTEZdTvuPOp4oHWoYGq7mga/uXtzTz7LQOD4RvC5tjVjRJgoeneb29QFqb36F/8zJ65UclwPMc/90QLy9Uy0pDA88qCPO16azkAhhE0nnVoloQeg0uAKpaDV5bPR6th+diRIsLW1VyLoY0ro6Iy6SxutVNrtUeXDcqAM3OoqrDka2OS0G3cTvQuXsi2l4Wj0Ev7cVmM6CoDAfTc3DTl9vRsXc82vc/hk73HMQnGw7rtfah2CjBs79Fo+m1+zH0Wk+0HHUId3994ceKe7i37Ry/JUDnHZh5s1W1ZzktijmGNo/swGVDS9B+eDKufDMa+89wkO6HLqpvRpJ7zHdWpWN9dyMkzB11Wh5F20vj0e3hA/jtQMUObF1QbKjXqaTnFeCBH3eb16gj5nGWgHa3HsbYH89s/40dXMOMUPbrJZO7GTR3N/fBCKtq03PUM7IaWg0yzz9Pq+Cr6QE07pON95bFoWWPeLTT58bnWyuuk8rZ6FArBJ0HmseTv9Wg3BFH0O2qIgwyr8EXSuuwQFw0MM+M+KwKCmrGof0V+bgi6tzuS9LqttiFQym2ibwAXLlNpPSQvahZIFIjE7DZ2G0+YR7G0LuKsOiBlgiu5CnUTtcm0tvdHX1bB2BL6H4c8TdvIC1i8cxT/ph6dRN4uNnfBeJCtb3bHJ+OYW/sxeHXzWM31by4Hg3Dob+9sNJ3L67uHIoAz/M///Cp8lJkFOPqD3bjpwnhwL4GwLEwZG0Jx49p0ejXzQf1gium9OS/TPhzPyY8WQSsbAEkVUPhnjCs35EMt2Zp6NOwjKq780Tm+K3VwsDmoL1qjt+qgxLx0TO1cWOHs5umdNnBZFzx0sHSNn4p5nceG4boteb1LPAgrusSDs8qpz8Pqvl6oa552GwN3o+0oD3wM4NG71o5yJjVGjhUR80fn7a+KhZhJwa3D0KNgIoptfmvubNv/2o3ZrxofhZpc5gUhrwdYVgdHYeoi4rQqvrpp+RrWzsA/k3ysNYvBnlVY1D/6jR8+VwD9Kp3/va7fO99WgQipvoRxPiYQXrzWNzyYBVkmrHYklcjgL31Ss+NzWGYn7kbl3bxQ2SQfZwbtuRa2jsqEHF1jmKHzAPf7AiuewD49n/NEeBx4dqdSy1Mr2YBSIw8hq0w70tND+OKe0qw4N6WCPQ8t39X7pOuPHe2fAF0nrly72x7drre2Y7mQvUCnrZun4Eax8xna93b0PJqvs9YfujC9LJNjS+7h3hsTraB3ltP/izuOcZ9i7bqrSpf5LhVJ39G8xX8yCq9hWN44s/tBnwzTs5Ll+3Ggczy9zaNzko10NE8nmz/XrVE461/9umtLrykpCTDDCT10skwuuz91+0De9x/GearwMgoyTPPDXN/2X5uryzjkd+2l25q97L1y7HJfXLQoEF6yfWwOpvK5cMNB/HMsp34bNshFMLxO5zYi0UxCXhy6Q68vDoa+9PPtE3W+ecl7T/9zfuRrcJC5BaWkX4OCkpKMG3dATy35gi+3inVcCf+/YIiA55BZVyiPAuRknHmHQr+OZKKJ5bswKTVe7DxWPmq5dfGpZX+7qo9WB9fRrs0U5h/2SVc6efQYF98v/MonjKPiSlr9yI+58K3JfTxMr9r3zK+19wiFJ3FqR6bUoQqPmUcM26VN398WQIDy270HJ9qf9e3VPOYKswrRHxGITz8yujE5VGI1HKcG5UpI6NIvcixMYikM1JQUoxLZqzF3beUYNJltXHLte5o9YJ0u3SMC5Y9e3v9Xgx5/AhevSQCTw+tii4P78VP+47qtRWrTXgwvDucPJCxe9dM1Ag4f80REnPy0f+jdXhwlAfeubYFRo0qQYtJa/XaUrUDfNC0ldxkbAKoNrHoWO/MmljM2noI/cdHY3L/CDwztBouvi8OM7ae2dRus7cfRv8Ju0t/9/Jq6HVPPD7abNX+TZPhkxBqMydzSCJ6tD/7KsUn/9yJqx9OwivmMTF2eCA6PLbnvAx+fzqdaoQC7eL0kkUhfLvlI/AsmjE0DvVH7TbyQGQTjHWNR1T1ip8//lS6RJn7yd/mAaHmEfRrfvqq7MoizTsjAn3RuLV0eLMZUL1dLNpHulYbbqpkukTSJT3++ONGv379jKysLJ1yXElJiTF9+nSjQYMGhru7u9G4cWNj1qxZeu3pOWN19lWzNhkIsR6c1nwFJRk9pp79YK0VzR6rs+fuiDNwqdUAuOpVZPjdvN6ISTt1FeKFHNR63Mqdhke/PQZ80g14ZhohY1ean/P8NmvoNmWdAf+kE/MdGm+M+GKT3qLUytgko/o9GwwEphnwMj/PoK3GzfNP3OZUlh40//7wjSf+G+aryoiNxqojpx9U+a/DyQauOvl33a7eaKw4lKS3Oq7BuL8NNDLPD58MA60OG01fX6HXlN+7aw8Y6Gg1sLR65Rqh96wzMgrO30DZZbntR/NY7LavtFrbL92o8fwKY8Xhk/N7pr7acdgIuXGLAW/z75mvKteuNyasqNgB/P+rOjulIM+IeGKtgTqJpcdY971G66kr9Vr7kpKS8u/9asnhRCP8bvPcCDA/s7f5GrLFuOunsx2AvOKlp6erl6NjdbaL+uGHH/DJJ5+gVq1aqFJGg/HJkydj7NixuOGGG9R2V1xxBe699168/vrregvXYKkw2RaXA6TV0EtaRjWs2+pC0ztdAHtSM4F1Zc3xG4L0vFNX9YT7Xbhxh164KAp/zAzFxD+PYuKyOPz9ZFuMbH52nTVOZefBAiDbZt7Z1BpYu+vEkpWLalfDmleaYsriRIz7Mw4LpoZj5vC2eu3p7UvPAjaf3POy5J/qOJZ5+und9kqTgk0n9xY1/q6Boxkn/+7Gpzrgy5+K8MDcHZg9B9jxSA+9pvx2JGeY//bxsSdL+SB1nS/ySy5sFeuMy9vgl6/88fj8aLz8x1GsH9sJPSPKmB/4DF3XPAKr36qPl5aUzh//+yt18WzPpnqtfQj19MaG51tj+s/ZePb3OMyZ4Y0tD16k19qvPhFh6tx4/c8EvGieGz+9WR0fDLGa5IGoArhkEDlx4kTcddddajaGsgLIo0eP4qWXXsJDDz2E8ePH46abbsJrr72G2267De+//z6ioy/88B32wtA/awZKDzbbG5iBgvyKHfftfLr5h+Nz/Cafh3xMWFE67/bFs/7CP/FWQ1icRrif+b2GljXHb1aZc/wm5eXhsi/+Qfuvd+DRP7ebKZY9dCJp+9f4nSXo+slKvLq6/Mdr78gwPNOjGZ7p3hTNwkqrx7YkpqPZe0vRxfyb0kbwXFQPKut4KsHRMsYRrBfkj4c7NcYLPaMwtInNg8xpVPUx/42QMoJFryxkFZ4+GFO/G1rGA5K3+bsFJwf3wV6eGBVVBy92qYMbWkSo3qBnSx0TIWUcj0YWzvO0z2UaUL86XuxaD092b4I6QT469exFVQ3E03r++H71Tx402x6E+3nj9tb1MKFXFK5pfm6z/VSk+sH+GNulMZ43H/yGlOPcIDpfXCqITE1NRfXq1fHee+/hjTfeQM2aNVFcfPLNZMaMGQgNDcX111+vU0q98sorOHLkCP744w+d4jrulWnUWtkEDi2j8fT1F36Wg/NNZtVxu3MFZo1qgOj7+uKzy5sjbMA2/LkvSW9RPul5hej1/lo8f70nYu7vi5U3X4Ru/RLx8MJdeotTu7RBDVS//Ij5zioYrJqITteXoLkO3iy+3HQU4bduxO83dMDuBy7FGwPqwm3YchScEIwZeHxhNDrcsgd7H+iLNbf3xJP9QtHo5b/0+rNh4JlfYtD2lt3Yc18frDX/5jP9q6HOiyv1+vK755JwoKlN+8K2uzBlhNW0k+eoe52qaDFUgnmrIN03HY2vzULv/xiCpUutULQeKu3krII570w0vDYD/RqdumQuM//cozwp9XUfYPPd1I7DJTf6ItynYobFycgvRkEZwTIRkTWXCiLT0tIwcuRILFq0SI3plJdXRgmQScZ5bNKkCUJCTpwmyc3NDW3atMHatSd2AChLUJB9NsouDymltZTUXtu6Fm552h0hl+8Dmu+F3/Bo3D2pBC8NbKzWOwLLPMDPL44xI7LWZnxg2b8+wOqWuHn6Xr1cPvP2HMOKT0OBIw10imlnM7z3WQEOZJ1+FokGwX6Yek8dNLzT/ExtzO+21QEMePkovrinKUK8T+zIMvbLw8C37c13UopnKg4ElrTBbfO2li6b4vMKMHW2+W/+0lmnmPLCsO/bWvhw40GdUD4phUWYMisLWNRJp5jyqiHu+whMW3dyR5Mz8XCvehj9dAn8B5q/33I/gq/ZjYde8sB9XW2r9s9edT8fvHF7JNo9an5vbcx/p9V+dBl3EF892Og/x9GTkqk3bo1Eh8fNAF8GkzZ/t+ML+83fbYx6QafuFFJWzUZ5tQgLwhsPhCHiJvN4bGW+Ou/HlS8nY/Ydzc6phLM85Fwpz7zZ9sz6OubonGm/OEtenOXYOltu0jBSv3d6hYWF6qC17PSmTZuic+fOmD59Onx9j99UZJDw1q1bq7aQfn7Hbxj5+fkYMmSI+v3ffvtNp55szpw5ePLJJxEeHo6SkhL1ksGU582bpwa8dhTyuRMTE1W7URhmPmDgQGY2UnILEeztgWahgdLVAMUyZP9/kLaVnu5uKhCXQ66w2LAue7ugqpj/uJeHO47GxiKibiT6fb0LW8b01WutDFyHork1EZt6+tIkS15kYHUP84+PW3sE065vCWTZ9IpsfAA/f1eAdtV8T5gxw/w1eJq/Z/ku5O8cNL/X+Jw89bebBgehqq8ncgpLP4ekuXkYiHwiDvi8u0qz1ujFFdh6f0Nk5JZgxbEMjLzHDD7XNNFrtSp5uPOLbXitX02k5515aZmXmc81SVkYfq95zqyynQklHzfP3oKpl9Uq198Usk+KzGPqUHYudh+MRVS9CDPf/uq4OIPD6YzJ5z+Wm4dDmaXBfP2AANQJ9EFWwemrs4Xt79YL8Fe9Yk/1u3JdOHz4MCIjI9W5c7Zkf3uY/7YcEwk5+eaxVsX8bgIR6OWBvAqoz5Z8JCQkqAdhGaTbkck5lpKSoq7vMgGEI5O8SEGIp6cn/P391bXDUUle5F4oP2UyC0fJi8QDU6ZMwYIFC+Dt7a0+v8QVEi/Mnj1bb+VizJ3nspo0aWJcf/31Rk5Ojk4pFRERYYwePfqkHn1mEGkMHDjQ6Nu3r04pm/TO/uWXX/SSYzt69Kh+d+5iMrKNjUlpxv6sih9gdntapvHbjj1GvlFiPP77TgO+aeZVS65c+uWda+DWxXrr/7YvI8fYYOblWEGe8W10rOHRff+Jf09el6w1tiWX3cN6e2qmsTk53Ticc+peo7ZaPr/BgGfOif+Gf7rR/r2/9BaGkVSQb4TfIIMQF524XYsY45nFZ9crNq2owKh+y7aT/2az/caj5nd5rhKOHtHvHJ8ZROp3jk16NBcVFeklxyY9muXa7QykN/Ppepo7EullXtbIKI6IvbPpBPIkbn436mXNkmYpyTwdRypxPBVLKeq5MzDuz2g0HrUX7bvHI+raQ7jjc+s5fy+cxNx83P39DrS89BAuuxaof0M0jqTkA5dJ1a4lb+bn6LgTb99+ZlXzLy/biyY3R6ND13jUu+IAvlicitqXyriOVs0jWu7BiOv8EBV6YtVnWl4h7p+/Cy2HHETbnkfR5uYDeGzBmXV8eWRoDVWt+i8P89/rsR0zrz4+T281Ty8MH+wO1JV2llpAKsIHJ+GBLmdXVRzs7okRgz3NL89qzmr/NAQPjMcj3evrhLOXewalgo7i/JwvlU/aipfVXtwRnb/rWOVzpv3iLHlxlmPrbDGILINU40gRtW0QKcync6dpk1JRpqw8iBefKgQWtgaimyF/YRRmTKiCsT/F6C0unP99GY0Pn/IH1rYAtjbB0S+a4svp7rjimkK0fnq7GUwuR9A96zB9ajgeuOi/Owl9tukInn4qB8Xz2gB7myFvUTPMezMIYWHA0KkHgMtXAsNW4YnXgC9uO7kN211z9uDdp72AVS1Vu8nUb6Lw+vhcfLvzvwcXv61zLbz6egCC71oPDPoLDR7djp/fa4w2NvP7TrqiPsa+WQRctQoYshJdnjuArS+2RQ3/s6/OG395PTw2xbxYXr1a/c2Oz+7D1oltUOsc/iYRETk2BpFl6NatG+Li4lT7E2sSVEq6dK6hMzdjjRkgSRBnbU8jTP3x7HpDl8f8hdnmv2Uz5t7vreBhxnFbXmoN49deSH+vM27vFKFXnt7HGw8Bq23GYtsViQ1/VcGCB6Ng/NgTxg898MqgpvByO/lhY+7P6WbwaNMDeV0bvLXqTGZRccPj/eoi7YOOKJ5TH/te7oiBjcP1uuPCfb3x+lWNYHzXA8ZPPfHP4+1Rw+/cgr1qPt6YfGVDGN92V39z3ZMdEBlgP7OOEBFRxWMQWYaePXti9+7dqlOJtUOHDqn0jh076hQ6E9X8ZMq0k0t1i3MNrE9KUfMDv7EmBnG6J/OOxEw8vrh0vuIVh08faE7fdAhPm7//6ZaDyCs5cUgSAyXwUeNb2irG3qOnH2z6VKrJGH5lVcMn5es3p+cXWNb0cQaOpZSvWueIHc7rS0REroVBZBkGDhyoel29+uqrOqXUY489hhYtWqBr1646hc5EzwbBQJjNnLzV04GITPS6+6iaH/jRYcG4+Kl9eOD3LRj45k681j8SzwwNQ787kjF5TVltBg0M+mwd7rytEC9fFoHbrvVEq+c3oRDHA0k38/Du0MIM2nzMf8tavcPo3cz8TGehV91qQA2r9obCPw21upUVrJ6sc3Pvk+fprRWLflFn93mIiIgqi0sHkdnZ2cjJyTmp7WONGjXw6aefYsWKFWq8SJn6sF69eti6dasKLBs0sBoPkP7TpAFN0XjMYaBpPOCVDreWRxH44Brgn/rI+a4lUBwEHAvHvln18M5bhTj8chfztwKB1Koo+q0Znhifi4Uxx0r/mHbb99vwyyO1gY2NgELz93fVxt6pjdDh5U16i1Jz7muEOveZQWiNFDVYNC7eg25Px+PNy2yq18/Q2O4N0eyhWKClGRSbeUGDY2jw7DbsGWc1huJpfHdfFCLu22sGjsnm72cAPfaizVMH8eHlnK6MiIgci0sHkTKWowSIMu6WLRkPcu7cuRgxYoQaK00GJ//yyy8xePBgvYXzk17o4aoq+txtfKITvppfhOd+P4qvvy3Gte2rA3/b9BaunQ0knNzGD3/XxuHUEweG3xKfBaTYzOecFYptm06s0o4I8Me6ca3w4a8ZGPPtDnw3PQir/9dNrz07Gx/thG++M/CsmZeP5+dh29huCPA4s5LIat7eWP9Ca0z/JbN0nt7pPtj8gP3P00tERGTLpQYbP1vSI9vD48yDKRm8XAYXl9lxKlNMahau/W4j3NzMoLhpOF68OEqv+W/70s3f/WYj8goLcWXL2hjf69S/+9TiXap3ccNQX7x+WRRah504009ZJv8TgyeGhZpBo9UUcpEpZiCZDvxjU9IbcQCvflWCx3se75AydNZ6LLy5rfnOZr8MXwxjfj+9cKL0hFgEV3eceXFPR9rn1q17/mZ3qUzMi/2RwcZlxi5HH2xcJCcnq8G5HX2wcSFT98o+kfw4OssweI4+u5sM8TN06FA1E54rYpvIM1CeANJevLb0IJrcug0b7rwY6++4GOMvqQn3+1eYa/77mWHK8oNodMs2rDN/d9u9/TDh0ppwu2u5uebE303OKUDLV/7BK9cHqDmjfxvdFW0uOYJJS63GMjyF4U1qwHuQTY9kowhodAwIyNQJIg/VRyRhWPPqernUvd0jgHY2c1M3j8H9N5+6l3XGeZjXmIiIiEoxiHRKxXjx8yTgB6t2egUhKPmpMZ5ftkcnnIqBcZ8nAvOteqCbv4ufm+KpJScGbZ9uOYwdn9UEjlkCNzdgcxQmfZqGtMLT91ZuVjUQk++phjo37gZamJ+pbQxGvhSPd8fWRK/HYs20GBUUNn1yJ756qB6iqp04peBgMwi95XF3BA+LBprugeeAXbh1fD6mXWkz3R8RERFdEAwindCBzFxkH5Y2ejYlqAdrYseh0wd3Sfn5yIyV37Vp43e4JrYfPPF3o1OzgV1mEHkCD2Sv80Genvf5dB7sWh9rP4zExmXh2Lo4DF/c0Ar3dqiPn55uiM3Lw7BpRTX89XwL9KtXRjtJ06ejorD5i1pYvzIcO+bUwScjWpqpMvMwERERXWgMIp1Q/UA/RDSWqmebsRAjjyEg2EBiQS7WJ6ZgX0aWXgEcyszBhsRUpBblm79bbB4ZhXqNVisePgEnjk3YsWYw0PzEsTSlFBQN0+FW5cyCuVq+fmgXFopWVUPgqaeTDPTwQptqIWhbLRRhvt4qrWxuqBcQgA7hoWgcHKjTiIiIqCIwiHRKVXDLUDOoanpIL5v8MoE++1FixoY1r9qHTj0T0Wr0EYz9bh/m7IxFu4f2oGP3BDQdHI/kIjP47Gw1T7IMjdP3ACZf1lwnlBrZohYC+8n4j1YllG13487RVVHDCRqxExER0akxiHRST1wSiefecAdG/wMMXoGLX9yHkYN9MftNf5QsbAnsaYbcn6Iw5bUiXDfxKFI/aa3mgsZyM31RE6CDGYDebP7u0FVo+VQ0NkxpjvpBJ05zF+rthYWPNUanF/cAQ1aYUeXfGP+GNz64rrHegoiIiJwVg0gnFeDpifFDG8D4vCuMhRdj+aNtsWVfPvCXTYBXrQD4UdoSWs3zfKCaGWSGw5jZEcZ3jbHthQ5oX6PsGVUurlcVa59vDeOni2HM7Ybn+jcyDyoeVkRERM6Od3sH9M2OODXf9Nvr9iEht3QQ7nVxaXhiSel80+vibabV0wJ8ytjdxWaadxnzMKcWICmvEImco5mIiIjKwCDSwYz5ZRuueTBVzTc95gp/XPxMDMb8sRWDXonG5P4ReObyauh991G8v+nksRp7NAoCqsbrJS0mBGgaqxcs8hHQtRDe7u4o4VD0REREVAYGkQ7kjb/34e3HvIE/9XzTsTWw5/M6ePv1IiRN6wwYZlpKNeT80AL3TcjA8kPJ+jdLvT28GRo9eLB0QG+Z97nlEXQfewSD7s2Ee5dDgI+ZFpyGWuPWYPkLzRDo6YViRpFERERUBgaRDuRgZjawrb5e0upkAUdq6IXjjL9r4GiGzRA/pg1PdcAXPxaoeZ8/+8rAqns6Y9ENnfDDV14YZ6ZN+T0JG8Z2Vm0gZTonIiIiorIwiLRze1Iy0e6j5eg56y/MjzkKhJa2gfxXljfgZTOmo/DORHZhkV44LsjLE9e3iMSEXlG4qXWkmVI6nuOQhjXxQs8oPNy5MWoGcHgeIiIiOj0GkXbs5cUH0OzWHdh8Vy/8dfNFOPxKe6B/tF6rFZUALczg0ssquPTKRP1rM9CvYTWdQERERHR+MYi0U4UoxkufpwA/Ws1hfSgciA8Crt4AtDKDyc4xGP1SEt55uAY6P3Lw3/mm2z0bgy/ub4D6wSeO60hERER0vjCItFNH1PzXXuY7m/mvVzbCoGElOLCmJrb/Go7PRrXAfR0b4LcX62PT8mpqvunFj7dEjzpV9S8QERERnX8MIu1ISl4B1iakYHtKOkL83NGspewem/aOkUdRO9QL9XwD0SI0GO5upbswxMtbzTUtL5lJhoiIiOhCYhBpJ9bHp6Lfa9vRpVsiWl0ajyEvHELtVtlAa5mbWvPNBC45hBf6cFpBIiIiqlwMIu3AnpRsXPP2Pmx+qQmwvxmwoRlWv1oPW/cU44YnsoAb16j5r9s8HY3tk1siMpBtHYmIiKhyMYi0A5sTU7Hv61pAfoBOMRX5IOm7SNzepzqMWV3U/Nebn+2AFmGBegMiIiKiysMgspLM0fNfT998EHFZefAJKR2v8QRFBYhNLmMMSCIiIqJKxiCyEty7cCuueyBNzX9953BfTJyVisKWtvNXm7qmIjLUWy8QERER2Q8GkRVs8qq9eP8xP2Bxi9L5rw9WR9JHbcy3mQgZsRvwyQQ8s+B39z/4+Olq6BXJAcOJiIjI/jCIrGC7Us0gcWc9vaTleQObq2HBtFC8svQoJi6Nxcrno3BHO5vtiIiIiOwEg8gLLKekEMPnrkOrD5fiiaU74CdDOAbll660ZmSjZ80wPNG1KZ7p0QztawXrFURERET2h0HkaRQXF2P//v3YsWMHDhw4AMMw9Jr/5ufljr/icuF/yxr8eG0LbL+7Dyb3r493Z+QCl+zWW2l1j2DojdLruozONZWoSpUq8PZ2njaZPj4++p3jY17sk7PkxcvLC+7u7nrJsXl6eqprmTOQvDjLfvHw8FAvcmwMIk8hKSkJjz76KLp164YOHTqgR48eeOyxx5CcnKy3OL1gX3c8MW8fMLetuaTHdSwxf/7WBu7NktH0tr1A1B6gWzSumpCCT29uYm5gX0FkYWEhvv/+e73k+L788kv9zvF99tln+p3jY17szx9//HHG1zp7t3LlSsTFWU3a4MDWrVuHffvM+4oT2L59u3qRY2MQeQrjxo3D9OnTMWvWLERHR2Pq1Kl49913MXHiRL3FqVVxc0NidgEOJRadOPajSPWHb2Ygds2oiw0rwrFjUXXMvbEVwnztr8SPQaT9mjlzpn7n+JgX+/Pnn3+qB2lnIEFkbGwZo184IAki9+7dq5cc27Zt2xhEOgEGkWVYu3atChi/+uorDBgwAJGRkRg5ciRmz56Njz/+GCtWrNBblq3EMBDm74V2dX0B7yydqvllISC8EG7wRPuwUDS3mv/a3riZwTCrGu2Tr695bDkJ5sX+OFt1NvNif6QqW/JDjo1BZBmk9K1p06bqZW3w4MGqjaAEmf8lM68YYy+rA7SzfmosBLrsxKfXNdfLRERERI6JQWQZtm7diiZNmqB69eo6pZQ0zo6KisLq1at1StlKSkpQxdMXvSP88cWnzdBq3CFg9A60eTkWy+a0x8CmYXpL+yalKs7SIF1IySoR/TcpIQoOdo4RIuTBPygoSC85NrkmBwTYNJFyUH5+furl6OQeKU2/XJWbUZ4uxy6ifv36qiPNjBkzTqieys/Px7Bhw1SvbWl4firSnkg65Xh6uCPAR15VzPduKCgykJlTguz8YjjCly7VJnIjSUlJ0SmOSwLIqlWrOk1ngbCwMKdps8a82B8573Nycpzi5igBpFy75eXoJICU+09ubq5OcVyWAFKOM0dWVFSEK6+8Ei+88IJOcS0MIstQt25d9OrVS3WssW5HV1BQgOHDh6uL0eLFi3UqERERkethdfYpSJW0bXwty/JypipeIiIiorPBaKgMUp1dVlWOBJB5eXlO076GiIiI6GwxiCxDu3btcPToUaSnp+uUUhJEyhhdLVq00ClERERErolBZBn69++PTZs2IT4+XqeUkukPjxw5omaxISIiInJl7FhTBultJYFkQkICfv75Z9WrNzU1FX369EHHjh3VrBTOMswCERER0dlgEHkKUhJ57733quprGXRcpmdq06YN3nnnHbRq1UpvRUREROSaGESehpQ+rlq1CjExMWrwcanGllJJIiIiIlfHIJKIiIiIyo0da4iIiIio3BhEEhEREVG5MYgkIiIionJjm8jzSDri/Pbbbzh27Bhq1qyJyy67DCEhIXqt/ZNZembPno1rr732lJ/7zz//xK5du9Tk+d27d0dUVJReYx/ks/3zzz/IyMhAaGgoevfujcjISL32REuWLFHbe3l5qU5TLVu21GsqX1JSkvp8Muh9jRo11PBS8rMsGzduVK+srCw1UL7M+26vZOzV7777DldddRVq1aqlU4+TsVhl/0lemjdvjn79+tnNNKNyqfzjjz/g4eEBNzc3nVo6JJic77ajNsjIDitWrEBmZiYaN26MSy+9VP2uPZHvWzoPFhQUqJm6Bg8erNec6PDhw1i8eLE6r+R8GjJkCDw9PfXayiPXWsmDsN4nQvaXpMnkENWrV9epUEO3/fLLL2oyCTkGL7/8cnh7e+u1lW/t2rXYunWrOgeaNWumzv2yPp/MqCbX4+joaAQHB+Oiiy5Co0aN9Fr7sGHDBqxfv159Vjk/TnVtkmmGJS979uyBv78/evTooUZFqWyW417uiT4+Pjr1ODm35Zog24WHh6Nv377qWlAWua7Jfs3Pz1dDBTrNeNMSRNK5i4mJMcwDyDCDKyMgIEC9zBPGME8KvYX9e+2114xq1aoZ5s1Pp5zohhtuUOuDgoJUPhs0aGDMmjVLr61877//vtGkSRPD19dXff/mSW+YQZXx008/6S2Ou/XWWw3zpDcCAwPV9uYN1HjnnXf02sq1adMmo1OnToZ5MVXftbzMYN3YvHmz3uK4uXPnGuZNXW0r+TVvlsa9995rmEGB3sK+PP7444a7u7thBi465bgFCxao/SfHlrzkWLv99tuN7OxsvUXlku9Uvl/5vs2A/t+XeQNXn9OaeWMxzJumOrYkL+ZDmTp/zAdNvUXlGz9+vFGvXr0Tvu9hw4bptcf99ddfhnnTU8eX5ZgcOXKkYQZweovKYz6QGLVr11b7xbI/zJu4ERERYZhBiDpvfvzxR721YZhBjWEGKIYZlKm8yMsMIo1Dhw7pLSrXu+++a9StW1d9LtknVatWNcwHrpOOm+LiYrUP5LiSa5hsbwaQxm+//aa3qHxTpkxR9wjzIV19Pjm+7rzzTiM3N1dvcdyoUaNUXi15adiwofHNN9/otZVHvns5XlJSUnTKceYDsTFo0KB/7/fykvvNli1b9BbHvffee4b5wPLvfUneP/roo3qtY2MQeR7ISdGlSxejffv2hvnEpdLkxte6dWsVSCYlJak0eyWfX27uoaGh6qQ/ePCgXnPcI488oi7U5tOiTjGMBx98UJ0U5pOzTqk8cjORG8Njjz2mU0oNGTJEXZS2b9+uUwxj4sSJKq/WN5ennnrK8PDwUDfMyiafd8CAAUZGRoZOKc2H3CSOHDmiUwxjyZIlKhCWfWcheZKgxvZ7sAezZ89WeZPv3nwq16mlZLlOnTrG//73P51iGMuWLVM3yfvuu0+nVK5ffvlFfbcffvihsXHjRvWZ5SUBsfXD4tatW9V5dM011+gUQ91Y5CYqDy/2YNq0aep8eeutt3SKYfz8889GWFiYutFb7Nu3TwVil156qU4x1PVBtrv22mv/vd5VFrm2yj74+++//90fEijKvpIgfvDgwUZaWpraVm76bdq0Mbp27aqWhQQHckOXQDInJ0enVo4ffvhBHe9jx47VKaXnhQTJ8vmsyXcvDwCSV4sbb7xR5cX6WldZ5ByR4HHMmDE6xTAOHDigrmFXX321Til19913q8+9cuVKnVKaJtcJOc8qgzxUXHHFFeozyLW3rIc/ube3aNHCSEhIUMvykNmnTx+jbdu2xuHDh1WamDdvntqvkydP1imGMXPmTHUtfPXVV3WK42IQeR78/vvv6ulCflpbvXq1Si+rJMxeSNAkJ4uUrvTu3VuVyNkGkXICyU3R+oIg8vPz1Q3mrrvu0imVR54IW7ZsaeTl5emUUrt27VIXKCl1ERKYSXB/yy23qGULuRlK6d91112nUyrHwoUL1dP4999/r1NKSaAiFzTrkl8J7OXiZOvZZ59Vwb09keC3WbNmqqSrrCDy+eefVwGabQnqK6+8ovKSlZWlUyqP3AQkCNm/f79OKZtsJ6V1tg+PUsokN47Y2FidUjnkHJFz4Oabb9Ypx0mJqgQjltJfKUGR71+CSWufffaZysvOnTt1in154oknVMmW5QYvLA8xUtJvTW7yUmIsgWhleuGFFww3N9XC7ATyQOjp6amXDJUnOVcmTZqkU0rJPpPgXv5OZZJzWGrlpPTaljzsSwmr5bhJTk5WQfKTTz6pli2kYEPuRQ8//LBOqRglJSWqBFTOc7kfyHki9xbbIFIeCmWffP311zqllFwbJHiW80NIibGcZ1KyaksCZSkxd3TsWHMemDd+mAcJ6tatq1NKdejQAeZJrdqE2CPzRMW4ceNgnhCq/d0ll1yi2kbZMoNhmCeDyo81aUso7VxkMHZpK1WZrrnmGkycOPGkdlrmxVa1VTFv3GpZ9oV81i5duqhlC2mrJvkzLwJISUnRqRWvZ8+eqk3UwIEDdUopaRMlbe9kP4i0tDSVl65du6pla507d1ZtwaT9jb146KGH1IxP5gMHzCBGp5aSNkJyjJkX7ZP2n+wn2Tf2cA5Ju9M6deqcso2txbJly1TbVDPA1ymlZF/JfpT9W5nMB0d1Dkg7L1vTpk3Dm2++qdo8C2njbd5I1TlkTfJiBmRYs2aNTrEfS5cuVXl48cUXT/jccp2WdrbmQ6VOKSXHmOwr88FGp1QOObfNe7JeOk72hbQptJA2eOZDykltcGU7aXsr7bzl2l5Z5LPKMS7tZm3J55Pvf/78+WpZ2gy7u7ur88Waj4+PassqbSSlbWhFkTa299xzDxo0aKDaQkr7Rss115ocS3K/l/xYk3bFZlCMzZs3q2W575gBs+o/YEuud7Kf5J7jyBhEngfSeFg6mMgNxpp0CJDGwStXrtQp9kemcZQOAJYG2WVdxKThtgQwEuDYks4o0qhYAsnKdMstt+CKK644qROGNNaWKSvNp0m1fODAAdUYWjps2JKLlnT8sDTUrwxyc5DG9L6+vmpZAi65yIwdO1bd7KQTgMjOzlb7RTpr2JIbpzy8/Prrrzqlck2YMEEFiXPnzlU3GGlEb03yKDc+6QRlq1q1aqpDkT3kRW6MMmPVe++9h/bt26NevXq4/fbb1U3CQvImwbt0DJCbozXZtxEREfj99991SuWQh0bpRCcPG3LtevDBB1VHp7fffludG/KdW8jNUG52EjBak2W5idrLMWbt6quvxrBhw3D33XfrlFLyINK2bduTZh2TwF4KASp7v8hnlvvIbbfdpjr9SKAv16+PPvoIjzzyiN4K6nom378cg7Yk4N+9e7fqkFdZ5B4iL9vj30LS5Z4h5LyX5bI6mcj1eN++fTh48KBOufDkWJCHCQlyAwMDTxnYy3kj578cN7bkc69bt07dM2U/yj1nwIABeu1xci2QwF8eehwZg8jzQJ42pLSkrF6kUrJS1pOMPZBAxboHXFkni0hMTFQnRFk9SyV/cuM81e9Wpri4ODz33HO4+OKLVSmrSE5OViVftiVeQtIsF0B7IMHslVdeqYIreSKX0hXLDV5KjCUvUhpsSy7Kcizaw3EnF+Tp06erEi4hx5EtSZMes2XtE8mH5Key8yIPF/I5pXRCSueuv/56XHfddarUUUqNpYezkGNHSjPK2i9SOix5Kes7qEhSii3f6+eff65KIy2fV4J9KT06cuSI3rL0HJJ1tj2fZVmuB5WdF1sffPCB+mw33HDDSdcryVdZx5glL5V9jElQP3XqVPz888+qpFcefOUYkwDk1Vdf1VtBBYiW88KWPVyP5XiRWoeygnIJGqWmx3LcyHkvn7ese6f8HcmH7UPnhRQaGlpmYGhL7vmW66wt2QeWY0lKGiWQLOt6YE/X6XPBIPI8sJwEZV1oJb0iT4ILQU5kyUtZFy25+Mr6yrxolUWGyJELsJR8vfzyy/+WpFg+a1kBseRP1tnL/pLSRikxlVJW+bzS9ECezIXlc5Z1U7Sni9Odd96pboISDFuzvfieKi/2cg5JoCVVoWPGjMG8efPw2GOPqRu7vJcbohxjUu1mOYbKOlckH/awX+S7lNecOXPw8ccf46uvvsIXX3yhfkqA8vTTT+stS7ctKy+W64E93QDlwerrr79WJflSqmfLkpdTXacrOy/yoCg1Q3KtknP+1ltvVQ+QUlL16aef6q1K8yHK2i+SJuvlGKwsch7Lw4mU3D/wwAM6FVi+fLl6UJH1ln1gyUtZ57693luEfG7L+WxLPrclX0I+f1n3G0sag0hSTxlyI7E+cIQsywFS1gHkSCwnuHW7HAtJkwtXWRe0yiLNB+RJXm6I8t66qkTyIid+WW0/JS+yzl7yIiUTEqyMHz9eVZlKCdgzzzyjjis5puS4k1JVW3LMyTZlXZgr0v/+9z/VtslSCinkc8n3a30syXd+qrxYzqHKzotUgy5atAhPPPHECeezVB9Ktam0l9y2bZtKk7yUda5IPuRVVqlERZLvWz6fBCoyBqHlmJfS+lGjRqnSY8mPkOo92db2Ri7Lcs2r7LxY++GHH1RVvVTP2waKwpIXOaas2UNepHmBBFybNm1STYOefPJJ3HHHHfj2229VupxLUkUq5HPKZ5ZjyZbkT/al7NPKJA9bUgu0YMECdb7IS9pDS7Mc63bclu+8rPNF0uzpemxNPrflfLYl9xbLNcLy+cu6tllKY+3pHDobDCLPA2lcK22JbDsMyIkuxdnSPs2RSUNhuYmX1eFELn5SLW5piF/Z5EY/cuRI1Xj7xx9/VO1WrElDafm8UlJpS/IiQY+0XbM38v3KQLZSHSRVQLIseZGmBrbk4isvaUtYWaTNkJQ8yAVSAi+5gdx3332qClWqjKZMmaICZKkmlv0h7YOket6WXGjlolyZefkvEmDKZ5dqYiFtBcvKi9xw5GZiPfB1ZZCSLrmx2XbMENL+Uc4DeQmp2ktNTf33hmdhyYs97Rc55k7VYUjIdVqqFm0DFgkq5dpdmftFPpcE7xIs2pJSVake/uabb9SyXNPk+5ffsSX7TdryyXWssskDr5R2SxvimTNnqg5B0qZb2kNaBuSWTmoS8MsxZkvyIseqpX24PZFjSWqKLOeJNbnnyzVOzjH5/NJGXa7ZtuT8kf3o6PEBg8jzQE5wKfWSQNKaHETyZCyNpR2ZdLqRvFiqUq3J07Gl80Nlk6pFaZQuN8fvv/9eVT/akouWnNhSdWRLbkLSm1uC5sry2Wefqc4aloDEmvQglYuOvCSIlB6E0sjelhyLEpxJcFNZ5ElcSunkc8o5IJ2A5DuXamE5lqRNkRxPcvOWEiI5xqRDgC0J9mVbOccqk5SoSOmQfLe2Dh06pG4Elg4bcr6X1dFMrg/SSaCy8yJBiHznZT2ASGAipSeWkizpJCAdu+SYsyY3StmnlXmMWZOgXXqKW5dy2ZLvXb5/21oICZDl4awy94t8BgmAywooJCiU88jyuWWfyPcv54Ut+Q7kAdp2ZICKJvtDznXZHxIYSxtV6Xgq1wA5zy29lSUYkyC+rM4zcm+RAMx2ZAB7IMeKnD9lFaxIBy65nklwLPcTyXdZnTWlw43sc9mfDs2gc7Zt2zY1UPVHH32kU0rJsozjZz5h6hT7JmMpypiKtuNEChkv68orr9RLpcwLr5pd4bnnntMplUdmCJHBnGWMu/9y0UUXGf3799dLpWSWHpnhQgZQr0zTp09XY9bJYLTWzBuIGl9R8mcGXirt5ZdfljrGE8YwMy/IxujRo+12/DEZ0FrGTpVjx5qMoWgGLieNwXjHHXeoceQq25w5c9T4nfKdW5Pv27yhGEOHDjXMIFGlzZo1S83KYz6UqGULObbMh62TxjKtaDk5OWpAZPnMtvr166cGFreMEyljKEperCcZEDIOo0w+YDsWZmUxA1p1rbUePN2WXCPkOi1jFVqT654ZvJ00FmZFMoMJNU5v586ddcpxcuzJuKNffvmlWpZjzgys1DiD1szgRY2NWdkzb8nnGzFihLoGmcGxTi0l1yYZcNyaGUiqGWusyT1VzvuXXnpJp1QOy/lgO06kGSCrY0nGsbUmkz34+/sbixYt0iml4/nKuJ75+fk6pXRMTxlAXu6rjs59nLTWp3Mi1SBS8iClSFKKJdUlMv6VNFAfPny46lxgebK3Z1L9KE9/0hZHnqCsyZPw+++/r56cZJ2UgD3//POq5GLGjBmVXuUgT7pS0iPtuqTkS9pCyrAy8pJ8SXWCpWRSnvZlOBN5WpYndnk6lnaHsg+lYb6UVFYWGatSqoD+/vtv9T3LsSRDxsg4i/JdSwcOKYEUUiUk43vKMCtSHSyll9L+0LzZ4I033qj0Eq+ySJsvKSWW3s3WQ2JJXuScsTRBkLzIcSUvaYwv1ayVSYaykg4O0i5VzgUhpVdSZSf75/XXX1cdOoSUBEnVpFQ/SomE5EX2qfS8lWuCjBZQmaRpihzjcj5LibUcZ9Jz+bXXXlNzSps3blWKLCQv0j5SjikZyUGOwZ9++gmTJk1S7d4sQ2dVNqlFkFEAHn300VP2rpVrs+wruU7LvpJrmZw/zz77rLpGSzOYyiIlw9L0Q6p9pbRbjjEp5ZIqYDn+pYmEGSCrbaWES0ou5dyQ60NAQIDKv5SUS2m4HIvy9yqLfD4pPZVrqRz7UrUrpabSaUjOg8mTJ59wbZJ8f/jhh6p6WH5P9pGl7bcco5VZNW8+EKp7txwb1p9Dzh/ZT3IsSfMn2Uau2dJER85vGZLJ0i5SziFprysjOFiaIMm5JmNNymgCUhrr0HQwSedInshlmjPzhFDTt8nTuyybF129hf2T6bbkkJCn+rLIDAnyRCylKfLTvBDbRSmrlF7J5zYvvGrGB3lv+5Lpz6zJvK7ydCilKVKCIU/HUlJhD8xgVk17KE+0cizJT/l8tiVbQp7YZRvZH1KKLNu++eabeq39kRJW2R8ypaEtKZ2UY0pmSJG8SImllEQUFxfrLSqXefE3zIdC9R3L55PvXEriZYo9W7IPZcYOKVWWEhUzcFMl9lKibC8+/vhjdfxLCb6UxElJt6TZkpoJmeLNDEzUsSYlxjKLSmWXqFqTef/luDIfIHVK2eLi4tQMJLI/JC/yO/fff/+/Ja+VTUpJZT/ISz6fnANSqmc9jZ6Qc0JmebEci/JTSrXkuLMXcq7L8W8GTuo4k2Psq6++0mtPNG7cOHXey7ZS4m8+8J80s1BlkO9U5sMuq8RdSo9lhifZR3KOy/khNVzJycl6i+OWL1+uSo/lXiP3TykxLutcc0RqjiXzRKLzRJ4QpUSrSZMmqu2XM5K2bPL0VVb7HUcj7VLkCVOeEO2NPIlLKamUQlhKv05F2g7Ky9Hb3wppZC/tqew5L9IeUEp9rAfmLouU3EmJhT3nRUoh5TbwXzPxSEm/lCg5wzEmpV7SwcNe8yI1J1JTUla7bltyjZA26ba1R/ZCJrOQ0sb/Or6EbCsll5b2xY5CaiWkhui/SoDluiYl4BIfOAsGkURERERUbuydTURERETlxiCSiIiIiMqNQSQRERERlRuDSCIiIiIqNwaRRERERFRuDCKJiIiIqNwYRBIRERFRuTGIJCIiIqJyYxBJREREROXGIJKIiIiIyo1BJBERERGVG4NIIiIiIio3BpFEREREVG5uhkm/JyKiM1RSUoL9+/fD398fNWrUwKZNm7B27VrUrVsX7du3V2lERM6MQSQR0VlIS/t/e3eMojAQhQH46apgo2IvYmmrnVew8DIeYE8iWHkCD6DgJbyDYKFiuZshsrLVJtsN3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unique orderings of vertices of a polygon","description":"Cody Problem 2671 asks us to determine whether four points can be the corners of a rectangle. The points are not necessarily input in order (either clockwise or counterclockwise). My initial attempt at the problem involved determining how the points might be presented. If the corners are numbered as shown below, then they can be input in 24 ways.\r\nHowever, for the rectangle problem, many of the 24 ways are essentially the same. For example, 2341, 3214, and 4123 are effectively the same as 1234 because the numbers of the corners could be shifted around the rectangle. In fact, only three of the 24 ways are different (1234, 1243, and 1324). \r\nWrite a function to determine the unique orderings of vertices of a polygon with  sides. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 356.917px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 178.458px; transform-origin: 407px 178.458px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/2671\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 2671\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 294.433px 7.91667px; transform-origin: 294.433px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asks us to determine whether four points can be the corners of a rectangle. The points are not necessarily input in order (either clockwise or counterclockwise). My initial attempt at the problem involved determining how the points might be presented. If the corners are numbered as shown below, then they can be input in 24 ways.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.133px 7.91667px; transform-origin: 383.133px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHowever, for the rectangle problem, many of the 24 ways are essentially the same. For example, 2341, 3214, and 4123 are effectively the same as 1234 because the numbers of the corners could be shifted around the rectangle. In fact, only three of the 24 ways are different (1234, 1243, and 1324). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 245.317px 7.91667px; transform-origin: 245.317px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine the unique orderings of vertices of a polygon with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.1667px 7.91667px; transform-origin: 22.1667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sides. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 182.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 91.4583px; text-align: left; transform-origin: 384px 91.4583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 262px;height: 177px\" 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data-image-state=\"image-loaded\" width=\"262\" height=\"177\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = polyVert(n)\r\n  y = nchoosek(2*n,n);\r\nend","test_suite":"%% Rectangle\r\nassert(isequal(polyVert(4),3))\r\n\r\n%% Triangle\r\nassert(isequal(polyVert(3),1))\r\n\r\n%% Heptagon\r\nassert(isequal(polyVert(7),360))\r\n\r\n%% Dodecagon\r\nassert(isequal(polyVert(12),19958400))\r\n\r\n%% Heptadecagon\r\nassert(isequal(polyVert(17),10461394944000))\r\n\r\n%% \r\nd = num2str(polyVert(19))-'0';\r\np = polyval(d(1:3:end),4);\r\np_correct = 3760;\r\nassert(isequal(p,p_correct))\r\n\r\n%% \r\nd = num2str(polyVert(15));\r\ns = polyVert(str2num(d(4)))+polyVert(str2num(d(6:7)));\r\ns_correct = 3113512920;\r\nassert(isequal(s,s_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-27T04:52:02.000Z","updated_at":"2026-01-15T18:13:53.000Z","published_at":"2021-05-27T04:56:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/2671\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 2671\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks us to determine whether four points can be the corners of a rectangle. The points are not necessarily input in order (either clockwise or counterclockwise). My initial attempt at the problem involved determining how the points might be presented. If the corners are numbered as shown below, then they can be input in 24 ways.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHowever, for the rectangle problem, many of the 24 ways are essentially the same. For example, 2341, 3214, and 4123 are effectively the same as 1234 because the numbers of the corners could be shifted around the rectangle. In fact, only three of the 24 ways are different (1234, 1243, and 1324). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine the unique orderings of vertices of a polygon with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e sides. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml 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sequence revisited","description":"This problem is related to \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42835-return-the-sequence-element-ii Problem 42835\u003e.\r\n\r\nFor any starting positive integer, a(1) = x, the \u003chttps://en.wikipedia.org/wiki/Juggler_sequence Juggler sequence\u003e is defined by:\r\n\r\na(i+1) = floor(a(i)^0.5) , for even a(i).\r\n\r\na(i+1) = floor(a(i)^1.5) , for odd a(i).\r\n\r\nWhen a Juggler sequence reaches 1, all subsequent elements will also be 1s.\r\n\r\nLet l(x) be the number of Juggler sequence iterations required to reach 1 with a starting value of x.\r\n\r\nLet h(x) be the maximum value of a Juggler sequence with a starting value of x.\r\n\r\nGiven x, return l(x) and h(x).\r\n\r\nExample:\r\n\r\nx = 3\r\n\r\nl = 6\r\n\r\nh = 36","description_html":"\u003cp\u003eThis problem is related to \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42835-return-the-sequence-element-ii\"\u003eProblem 42835\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eFor any starting positive integer, a(1) = x, the \u003ca href = \"https://en.wikipedia.org/wiki/Juggler_sequence\"\u003eJuggler sequence\u003c/a\u003e is defined by:\u003c/p\u003e\u003cp\u003ea(i+1) = floor(a(i)^0.5) , for even a(i).\u003c/p\u003e\u003cp\u003ea(i+1) = floor(a(i)^1.5) , for odd a(i).\u003c/p\u003e\u003cp\u003eWhen a Juggler sequence reaches 1, all subsequent elements will also be 1s.\u003c/p\u003e\u003cp\u003eLet l(x) be the number of Juggler sequence iterations required to reach 1 with a starting value of x.\u003c/p\u003e\u003cp\u003eLet h(x) be the maximum value of a Juggler sequence with a starting value of x.\u003c/p\u003e\u003cp\u003eGiven x, return l(x) and h(x).\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003ex = 3\u003c/p\u003e\u003cp\u003el = 6\u003c/p\u003e\u003cp\u003eh = 36\u003c/p\u003e","function_template":"function [l h] = juggler(x)\r\n  l = x;\r\n  h = x;\r\nend","test_suite":"%%\r\nx = 3;\r\nl_correct = 6;\r\nh_correct = 36;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 5;\r\nl_correct = 5;\r\nh_correct = 36;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 10;\r\nl_correct = 7;\r\nh_correct = 36;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 77;\r\nl_correct = 19;\r\nh_correct = 2322378;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 99;\r\nl_correct = 11;\r\nh_correct = 37754276;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 117;\r\nl_correct = 11;\r\nh_correct = 44992;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 1;\r\nl_correct = 0;\r\nh_correct = 1;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 2;\r\nl_correct = 1;\r\nh_correct = 2;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-27T19:30:07.000Z","updated_at":"2025-12-31T12:07:49.000Z","published_at":"2016-04-27T19:30:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is related to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42835-return-the-sequence-element-ii\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 42835\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor any starting positive integer, a(1) = x, the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Juggler_sequence\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eJuggler sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is defined by:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(i+1) = floor(a(i)^0.5) , for even a(i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(i+1) = floor(a(i)^1.5) , for odd a(i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen a Juggler sequence reaches 1, all subsequent elements will also be 1s.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet l(x) be the number of Juggler sequence iterations required to reach 1 with a starting value of x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet h(x) be the maximum value of a Juggler sequence with a starting value of x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven x, return l(x) and h(x).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003el = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eh = 36\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61052,"title":"Compute the Dedekind psi function","description":"Write a function to compute the Dedekind psi function. The values for n = 1, 2, 3, 4, 5, and 6 are 1, 3, 4, 6, 6, and 12. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 10.5px; transform-origin: 408px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/DedekindFunction.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eDedekind psi function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The values for n = 1, 2, 3, 4, 5, and 6 are 1, 3, 4, 6, 6, and 12. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = DedekindPsi(n)\r\n  y = psi(n);\r\nend","test_suite":"%%\r\nn = 1;\r\ny = DedekindPsi(n);\r\ny_correct = 1;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8;\r\ny = DedekindPsi(n);\r\ny_correct = 12;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 49;\r\ny = DedekindPsi(n);\r\ny_correct = 56;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 312;\r\ny = DedekindPsi(n);\r\ny_correct = 672;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1441;\r\ny = DedekindPsi(n);\r\ny_correct = 1584;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8028;\r\ny = DedekindPsi(n);\r\ny_correct = 16128;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 14035;\r\ny = DedekindPsi(n);\r\ny_correct = 19296;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 85432;\r\ny = DedekindPsi(n);\r\ny_correct = 131040;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 6645344;\r\ny = DedekindPsi(n);\r\ny_correct = 10402560;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 5533221188;\r\ny = DedekindPsi(n);\r\ny_correct = 9083498112;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\np = primes(1e8);\r\nq = p(randi(length(p)));\r\ny = DedekindPsi(q);\r\nassert(isequal(y,q+1))\r\n\r\n%%\r\np = primes(200);\r\nq = p(randi(length(p)));\r\nn = randi(5);\r\nx = q^n;\r\ny = DedekindPsi(x);\r\nassert(isequal(y,x+x/q))\r\n\r\n%%\r\np = primes(200);\r\nk = unique(randi(length(p),[1 randi(5)]));\r\nq = p(k);\r\nx = prod(q);\r\ny = DedekindPsi(x);\r\nassert(isequal(y,prod(q+1)))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2025-10-25T15:14:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-10-25T15:09:34.000Z","updated_at":"2026-02-26T13:49:01.000Z","published_at":"2025-10-25T15:14:46.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/DedekindFunction.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDedekind psi function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The values for n = 1, 2, 3, 4, 5, and 6 are 1, 3, 4, 6, 6, and 12. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47295,"title":"Find Logic 13","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 221.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 110.81px; transform-origin: 174px 110.81px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 100\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 102\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 99\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 103\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 98\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of logic\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 100;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 100;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\nassert(isequal(logic(x),102))\r\n\r\n%%\r\nx = 4;\r\nassert(isequal(logic(x),103))\r\n\r\n%%\r\nx = 7;\r\nassert(isequal(logic(x),97))","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":403,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-05T07:07:30.000Z","updated_at":"2026-02-14T07:02:11.000Z","published_at":"2020-11-05T07:07:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 102\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 99\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 103\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 98\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of logic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51274,"title":"Solve a nonlinear difference equation","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 95.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 47.875px; transform-origin: 407px 47.875px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 44.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.25px; text-align: left; transform-origin: 384px 22.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.967px 7.91667px; transform-origin: 102.967px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider the difference equation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-8px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a_{n+1} = a_n^p\" style=\"width: 60.5px; height: 22px;\" width=\"60.5\" height=\"22\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.2333px 7.91667px; transform-origin: 48.2333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the initial (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n = 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.95px 7.91667px; transform-origin: 22.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.70833px 7.91667px; transform-origin: 9.70833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 7.91667px; transform-origin: 28.3917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 2 and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = 2\" style=\"width: 38px; height: 18px;\" width=\"38\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 7.91667px; transform-origin: 19.4417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a1 = 4\" style=\"width: 41.5px; height: 20px;\" width=\"41.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a2 = 16\" style=\"width: 49px; height: 20px;\" width=\"49\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a3 = 256\" style=\"width: 56.5px; height: 20px;\" width=\"56.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.1px 7.91667px; transform-origin: 17.1px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, etc. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.125px; text-align: left; transform-origin: 384px 21.125px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.492px 7.91667px; transform-origin: 125.492px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes two values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.475px 7.91667px; transform-origin: 103.475px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the corresponding values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABNklEQVRYhe2VUbWDMAyGPw84wAAGqgAFOKgDHMwCGpBQD1hAAxbYA8lpxsrY4ZTdh9vvnD4sWfPTpEmhUCgUCoU/ogE80ANObE5+N3eKBmAWcQcMwASssuo7hDsJPgPVzrca30+Frfgjt3BrgruEvz7xX6YCFgk8HvxHs7KQzspleuKpjm5xEH/IKQzx1EeBnfm4PqfwN4ED55m5hE15m/B7YmZurfdevGNru5HXsgzELPXin9hasBL/KraPNEY8yOZKgmq/68kHWfuO0LK04nfEaXg6CfVkdo3EFC87+55FPjQQZ8As66sx3LKd1ic2fHpMbOa82HQgHc2MbOidmYiZ0oHkjzblQuvdGZteuNueXSX1EM3GlmrfLOiAsrXVOzCwtd5t4g/e50PNdvsXXktRKBT+CU+MO3Oqf1KjkgAAAABJRU5ErkJggg==\" alt=\"a_n\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.5833px 7.91667px; transform-origin: 85.5833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand returns the initial value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.225px 7.91667px; transform-origin: 27.225px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the exponent \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p,a0] = recurrence1(n,a)\r\n  p = f1(n,a);\r\n  a0 = f2(n,a);\r\nend","test_suite":"%%\r\na = [16 65536];\r\nn = [2 4];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 2;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [512 134217728];\r\nn = [2 3];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 3;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [4.756828460010884 2684.848561202718];\r\nn = [2 6];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 3/2;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [4.756828460010884 2684.848561202718];\r\nn = [2 6];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 3/2;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [0.840896415253715 0.999994711720674];\r\nn = [2 17];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 1/2;\r\na0_correct = 1/2;\r\nassert(abs(p-p_correct)\u003c1e-10 \u0026\u0026 abs(a0-a0_correct)\u003c1e-10)\r\n\r\n%%\r\na = [3.236570233533632 6.5197372744901154];\r\nn = [53 100];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 1.01;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [27.065907669081142 6576132142.795870];\r\nn = [4 8];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = (1+sqrt(5))/2;\r\na0_correct = (1+sqrt(5))/2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [1.033024879021228 1.000000123944382];\r\nn = [2 8];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 1/8;\r\na0_correct = 8;\r\nassert(abs(p-p_correct)\u003c1e-10 \u0026\u0026 abs(a0-a0_correct)\u003c1e-9)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-04-02T16:23:14.000Z","updated_at":"2026-01-13T13:35:21.000Z","published_at":"2021-04-02T16:27:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the difference equation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a_{n+1} = a_n^p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_{n+1} = a_n^p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with the initial (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 2 and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = 2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a1 = 4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_1 = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a2 = 16\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_2 = 16\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a3 = 256\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_3= 256\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, etc. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes two values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the corresponding values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a_n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand returns the initial value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the exponent \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47370,"title":"Find Logic 25","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 191.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 95.8333px; transform-origin: 174px 95.8333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(11) = 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(15) = 6\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(22) = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return value according to logic in problem\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 11;\r\ny_correct = 2;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 15;\r\ny_correct = 6;\r\nassert(isequal(logic(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":234,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-06T13:48:01.000Z","updated_at":"2026-02-14T13:45:20.000Z","published_at":"2020-11-06T13:48:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(11) = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(15) = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(22) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return value according to logic in problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":47345,"title":"Find Logic 20","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 251.571px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 174px 125.786px; transform-origin: 174px 125.786px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGuess the Logic!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(1) = 7\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(2) = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(3) = 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(4) = 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(5) = 9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9524px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 10.4762px; text-align: left; transform-origin: 151px 10.4762px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elogic(6) = 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9048px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 151px 20.9524px; text-align: left; transform-origin: 151px 20.9524px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = logic(x)\r\n  y = 7;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 7;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 4;\r\nassert(isequal(logic(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\nassert(isequal(logic(x),9))\r\n\r\n%%\r\nx = 6;\r\nassert(isequal(logic(x),2))","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":293792,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":365,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-06T05:30:27.000Z","updated_at":"2026-03-17T20:15:27.000Z","published_at":"2020-11-06T05:30:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGuess the Logic!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(1) = 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(2) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(3) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(4) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(5) = 9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elogic(6) = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function logic(x) which will return 'x' th term of sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56593,"title":"List the nth term of Rozhenko’s inventory sequence","description":"Consider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\r\n0\r\n1, 1, 0\r\n2, 2, 2, 0\r\n3, 2, 4, 1, 1, 0\r\n4, 4, 4, 1, 4, 0\r\nWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19th term is 4. \r\nThis sequence produces interesting plots and music. See the related Numberphile video for more. \r\nWrite a function to report the th term of this sequence. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 345px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 172.5px; transform-origin: 407px 172.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.6px 8px; transform-origin: 374.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1, 1, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.2167px 8px; transform-origin: 27.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2, 2, 2, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7667px 8px; transform-origin: 42.7667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3, 2, 4, 1, 1, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7667px 8px; transform-origin: 42.7667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4, 4, 4, 1, 4, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e term is 4. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.425px 8px; transform-origin: 112.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis sequence produces interesting \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A342585/graph\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eplots\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/play?seq=A342585\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003emusic\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.275px 8px; transform-origin: 18.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. See \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=rBU9E-ZOZAI\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ethe related Numberphile video\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.8833px 8px; transform-origin: 31.8833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for more. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.1px 8px; transform-origin: 90.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to report the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.5583px 8px; transform-origin: 78.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term of this sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Rozhenko(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 19;\r\ny_correct = 4;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 53;\r\ny_correct = 5;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 347;\r\ny_correct = 25;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 823;\r\ny_correct = 27;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 1997;\r\ny_correct = 20;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 4721;\r\ny_correct = 68;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 13859;\r\ny_correct = 18;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 19793;\r\ny_correct = 7;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 24677;\r\ny_correct = 51;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 41903;\r\ny_correct = 357;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 25537;\r\ny_correct = 4;\r\nassert(isequal(Rozhenko(Rozhenko(Rozhenko(n))),y_correct))\r\n\r\n%%\r\nn = [1 4 8 14 20 28 37 46 57 69 82 95 110 125 142 159 177 196 216 238 260 285 310 335 362 390 418 448 478 511];\r\na = arrayfun(@Rozhenko,n);\r\ns_correct = 0;\r\nassert(isequal(sum(a),s_correct))\r\n\r\n%%\r\nfiletext = fileread('Rozhenko.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-11-13T14:07:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-11-13T04:07:55.000Z","updated_at":"2026-01-24T12:19:36.000Z","published_at":"2022-11-13T04:08:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1, 1, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2, 2, 2, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3, 2, 4, 1, 1, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4, 4, 4, 1, 4, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e term is 4. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis sequence produces interesting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A342585/graph\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eplots\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/play?seq=A342585\\\"\u003e\u003cw:r\u003e\u003cw:t\u003emusic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. See \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=rBU9E-ZOZAI\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ethe related Numberphile video\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to report the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term of this sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60266,"title":"Stern-Brocot Sequence","description":"The Stern-Brocot diatomic sequence is defined as follows:\r\n\r\nThe first elements of the sequence are 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3.\r\nWrite a function to compute  for a given .\r\nSee https://oeis.org/A002487","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 214.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343.5px 107.25px; transform-origin: 343.5px 107.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.5px; text-align: left; transform-origin: 320.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Stern-Brocot diatomic sequence is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 93px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 46.5px; text-align: left; transform-origin: 320.5px 46.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-41px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"115\" height=\"93\" style=\"width: 115px; height: 93px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.5px; text-align: left; transform-origin: 320.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first elements of the sequence are 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 11.25px; text-align: left; transform-origin: 320.5px 11.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14\" height=\"20\" style=\"width: 14px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for a given \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320.5px 10.5px; text-align: left; transform-origin: 320.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSee \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A002487\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://oeis.org/A002487\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = stern_brocot(n)\r\n\r\nend","test_suite":"all_glo = [0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4, 9, 5, 6, 1, 7, 6, 11, 5, 14, 9, 13, 4, 15, 11, 18, 7, 17, 10, 13, 3, 14, 11, 19, 8, 21, 13, 18, 5, 17, 12, 19, 7, 16, 9, 11, 2, 11, 9, 16, 7, 19, 12, 17, 5, 18, 13, 21, 8, 19, 11, 14, 3, 13, 10, 17, 7, 18, 11, 15, 4, 13, 9, 14, 5, 11, 6, 7, 1, 8, 7, 13, 6, 17, 11, 16, 5, 19, 14, 23, 9, 22, 13, 17, 4, 19, 15, 26, 11, 29, 18, 25, 7, 24, 17, 27, 10, 23, 13, 16, 3, 17, 14, 25, 11, 30, 19, 27, 8, 29, 21, 34, 13, 31, 18, 23, 5, 22, 17, 29, 12, 31, 19, 26, 7, 23, 16, 25, 9, 20, 11, 13, 2, 13, 11, 20, 9, 25, 16, 23, 7, 26, 19, 31, 12, 29, 17, 22, 5, 23, 18, 31, 13, 34, 21, 29, 8, 27, 19, 30, 11, 25, 14, 17, 3, 16, 13, 23, 10, 27, 17, 24, 7, 25, 18, 29, 11, 26, 15, 19, 4, 17, 13, 22, 9, 23, 14, 19, 5, 16, 11, 17, 6, 13, 7, 8, 1, 9, 8, 15, 7, 20, 13, 19, 6, 23, 17, 28, 11, 27, 16];\r\nn = randi([101,numel(all_glo)]) \r\ny_correct = all_glo(n+1)\r\n\r\n%%\r\n% n and y_correct are displayed but their definition is hidden.\r\nn\r\ny_obtained = stern_brocot(n)\r\ny_correct\r\nassert(isequal(y_obtained,y_correct));\r\n\r\n\r\n%%\r\nn = 100\r\ny_obtained = stern_brocot(n)\r\ny_correct = 7\r\nassert(isequal(y_obtained,y_correct));\r\n\r\n%%\r\nyy_correct = [0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3];\r\nfor n = 0:numel(yy_correct)-1\r\n    y_obtained = stern_brocot(n);\r\n    y_correct = yy_correct(n+1);\r\n    assert(isequal(y_obtained,y_correct));\r\nend\r\n\r\n%% \r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-11T16:21:06.000Z","updated_at":"2026-03-24T12:11:40.000Z","published_at":"2024-05-11T16:21:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Stern-Brocot diatomic sequence is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$$\\\\begin{cases} s_0=0,\\\\\\\\   s_1=1,\\\\\\\\ s_{2n} = s_n,\\\\\\\\ s_{2n+1} = s_n+s_{n+1} \\\\end{cases}$$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first elements of the sequence are 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for a given \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A002487\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://oeis.org/A002487\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50913,"title":"Compute the nth term from the golden sieve","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.5px; transform-origin: 407px 82.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45367\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 45367\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129.5px 8px; transform-origin: 129.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved the Sieve of Eratosthenes, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/50811-compute-the-nth-term-from-the-sieve-of-flavius-josephus\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 50811\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94px 8px; transform-origin: 94px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved the Sieve of Flavius Josephus. To apply the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003egolden sieve\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133.5px 8px; transform-origin: 133.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, start with the natural numbers and at the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129px 8px; transform-origin: 129px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth step, take the sequence, which we will call \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87px 8px; transform-origin: 87px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and delete the term in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a(n)\" style=\"width: 29.5px; height: 18.5px;\" width=\"29.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.5px 8px; transform-origin: 30.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e position. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 119.5px 8px; transform-origin: 119.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the first step, delete the term in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHAAAAAlCAYAAACao20PAAACgElEQVR4nO2abbGjMBRAj4c4WAMYQEEV4AAHdYAFNCABD7WABix0fyQZ8vqSlnywhO49M8y8eSUh5OTjXgAEQRAEQTgaBfQF62uBpmB9whsUMFO2wxUwAV3BOgUPCngQL2/P+bbub5RYzeoyA/eI81tTZt15vgIWKrrhTDr0/UxnNwS0uGXnuQ1a3NMcewWC3lsfcU2rjhu6r+z9ny5QoSXsWd56tOybKRMrEPTNx8z0mhjQfdBTkcCY2ediZ2GswHtCmRqpRuCKHlmxpAr8Y8pdPaCpQuDNNOKWUDZVIFS0+WdwqMAGHSUq538tevS7DKYRinhyBE6J5WqiuEDFtr9M5u+ZTdKT3yG8lZBCjsC7Kfs6oPZgB2fukUtRgQ1baOtKUrwP91e0iBRKCEzpSDeFST1KzP5iAhu2kN6XJNsLjYHfzhDYkh7IDObaOUeJWVNEoCvP1xnuDPT9frbAq+aDUEjgw1QSerpho8xQoCIC08kW2DmVhNKAkfeCzxKYk77UQrZAG7SEnqLYhPlJOFFfuF4Q8xVRaMNnOaNzTqjBZ6cROfnnpaNQ92Gqbxlq+dngUEfl5GM5AmfSnr/Cl0ShtuN9Am1kOvFz/+v4/amEncn/+lHaij+tuRJZAt3o0l1CW3TnuIn9wPby0TcTF9I6M1WgXR1K7ENnUiyIsbPswSbPvcBKWB5sj99i9qPXJTpGxkj68lkL7gq4kLYFodj2A99HQ735ree9nJgXui1agG9fGfi8FNtrXTV96NB97bv/Oyd+LmLfsKdEhTHYASccwMixgYXdn48eJP81M8e8Kf+2L9KqZqSsxCM+FhY+UDLIeP0yQBAEQRAEQbgKfwHdzFGGzPiz9wAAAABJRU5ErkJggg==\" style=\"width: 56px; height: 18.5px;\" width=\"56\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 231.5px 8px; transform-origin: 231.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e position to get 2, 3, 4, 5, 6, 7,…Then in the second step, delete the term in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a(2) = 3\" style=\"width: 56px; height: 18.5px;\" width=\"56\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 256px 8px; transform-origin: 256px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e position (i.e., 4) to get 2, 3, 5, 6, 7, 8, 9,…In the third step, delete the term in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHAAAAAlCAYAAACao20PAAADG0lEQVR4nO2a4bGrIBCFvx7swAZswApSQTqwg3RgC9aQEuwhLaSGtHDfD9mRKMiK+NQMZ4aZzEQQWPbs2UXIyMjIyMjI2BsF0CQcrwaqhONlLKAAetJueAE8gXvCMTMcKIAXeuPVphUrxv4FIxaMa5+2G9AeNbEeeASeqRi86W/SeqAM9C2AN9en0wfz9dutPmpS78AzFfAxzz1MezFO/EPYGxvT56ooGNbpM15/5KSW6E2ecYmbO+MCQh4M4wG4IuSga8LGf4PG+x4sK9M3gwGfyvd9dFM7HT4cGON80EwqlFb0DAbULK40z15N0AjTNJwojt8YJnXbOI54oHZhb3TeeibIGu2Y37GTMSvmEr9mrhRbM5ktnF6j9z7Bk2vRqB3nXa0jQVwsGOPL0/zuGY3k8hChvliIMl0rSkSKh1IP3zt9ediathal6dfgT6WijVjhprGCb5ef4kOc9C2Z50Mt+gVI35iNlEO3paXw/pK5IaPUtXiBLwbZbu76b60B76aPnQOuPYVCuzFCpjXv2dJSxl+bXjW58Bds47k2w/ZA1/9bk0+hbduImkK4GPCq+eAUdphaxSriBb7qhqhMn1BJVT2w36MZ79cMKKmR9gAD367rSwM6lg2csvwjh0kTX1KlL2eCrF9tQBEtviqKfSp8Ev9NOgMKlWoMuEXEHKVCQxBxpYrrFWHjdIR5eWsaYUOMoi2nxeafZ1GhU4gHqlKjxpqMi4Zqvifs26gt+dgUcmA0tNgTrr/6cDYVCiPbqW9abOU33TBRppKjyKB35vwsnrw1FslthTaNkDLUVSC07YMcXjU126rPptCaYXPsxL5lMJ7vGuRNeDOFHlwXt3Lbrr2sFXY45OIzAjbbudYoYnK1oraLqy/TxHjwzfdLd1hSflvynGkhtzP9WvPfmipMRzx9HoFpOLLXL6EgisEKxnjg+mioMf81LG+u5kK3ZB57HqbPGiEi77pa+rC0/lPgRkQZKAKyCRk7oGNfYSHx+VSfI/waevahhV/5Iu0S6EhrxD0+Fs4IIKXI0H78m5GRkZGRkZGRcTb8A/oNdpREGA/GAAAAAElFTkSuQmCC\" alt=\"a(3) = 5\" style=\"width: 56px; height: 18.5px;\" width=\"56\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.7167px 8px; transform-origin: 52.7167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e position (i.e., 7) to get 2, 3, 5, 6, 8, 9, 10,…Et cetera.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102px 8px; transform-origin: 102px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 178.5px 8px; transform-origin: 178.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term in the sequence after an infinite number of steps.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = goldenSieve(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 6; \r\ny_correct = 10;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 16; \r\ny_correct = 26;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 60; \r\ny_correct = 97;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 616; \r\ny_correct = 997;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1666; \r\ny_correct = 2696;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 6066; \r\ny_correct = 9815;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 16166; \r\ny_correct = 26157;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 66616; \r\ny_correct = 107787;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 166666; \r\ny_correct = 269671;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 606606; \r\ny_correct = 981509;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 161161616; \r\ny_correct = 260764972;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 6161161616; \r\ny_correct = 9968968905;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 616161161616; \r\ny_correct = 996969702042;\r\ny = goldenSieve(n);\r\nassert(isequal(y,y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-12T02:43:21.000Z","updated_at":"2025-12-17T13:39:40.000Z","published_at":"2021-03-12T02:52:22.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45367\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 45367\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved the Sieve of Eratosthenes, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/50811-compute-the-nth-term-from-the-sieve-of-flavius-josephus\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 50811\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved the Sieve of Flavius Josephus. To apply the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egolden sieve\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, start with the natural numbers and at the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth step, take the sequence, which we will call \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and delete the term in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e position. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the first step, delete the term in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e position to get 2, 3, 4, 5, 6, 7,…Then in the second step, delete the term in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a(2) = 3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(2) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e position (i.e., 4) to get 2, 3, 5, 6, 7, 8, 9,…In the third step, delete the term in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a(3) = 5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(3) = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e position (i.e., 7) to get 2, 3, 5, 6, 8, 9, 10,…Et cetera.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term in the sequence after an infinite number of steps.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":48025,"title":"Find the Pattern 2","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 141px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 70.5px; transform-origin: 407px 70.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the pattern for the following sequence:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(1) = 98\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(2) = 92\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003epat(5) = 50\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCreate a function which satisfies the pattern shown above.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pat(x)\r\n  y = x+2*x+3*x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 98;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 5;\r\ny_correct = 50;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 11;\r\ny_correct = -142;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 3;\r\ny_correct = 82;\r\nassert(isequal(pat(x),y_correct))\r\n%%\r\nx = 3.5;\r\ny_correct = 75.5;\r\nassert(isequal(pat(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":180632,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":237,"test_suite_updated_at":"2020-12-17T19:02:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-17T18:57:25.000Z","updated_at":"2026-03-20T14:58:53.000Z","published_at":"2020-12-17T19:02:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the pattern for the following sequence:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(1) = 98\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(2) = 92\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003epat(5) = 50\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a function which satisfies the pattern shown above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52283,"title":"Find numbers in the Popular Computing Z-sequence","description":"Here’s a quick one. In 1977 the magazine Popular Computing sought “problem situations for which the computer is the best (if not the only) tool for solution” and proposed the Z-sequence as a candidate “problem situation:”\r\n and  for \r\nAmong the Z-sequence’s properties, the magazine staff pointed out that “successive values seem unpredictable; that is, the values jump around, but not too wildly” and “almost every integer appears as a term in the sequence sooner or later, except for a few numbers, such as 245, 449, 569, 575, and 903.”\r\nWrite a function to find the index of the first occurrence of  (including the five numbers above) in the Popular Computing Z-sequence. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 195.817px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 97.9083px; transform-origin: 407px 97.9083px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130.958px 7.79167px; transform-origin: 130.958px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHere’s a quick one. In 1977 the magazine \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.9167px 7.79167px; transform-origin: 59.9167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ePopular Computing\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.533px 7.79167px; transform-origin: 192.533px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sought “problem situations for which the computer is the best (if not the only) tool for solution” and proposed the Z-sequence as a candidate “problem situation:”\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.9083px; text-align: left; transform-origin: 384px 10.9083px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJEAAAAoCAYAAAD+HRieAAACw0lEQVR4nO2ZUbXCMAyGPw9zMAMzMAUowMEc4OBamAYk4AEL0zAL3IeS0wzaDdbCKOQ7py/s3nbJ/qRJC4ZhGIZhGIZhGIZhfDY1sN/6JYwyqYEeuADHjd/FKIwK+MOJR4aJyHiKA9Bch4nISMZEZCRjIjKSeYmIGqDD7Zvt9bcWv49+K9LmHvDtrvhit9VLvYGsImqAEzDgHNfi2r+zWqjOsZCixn201NHeTvwEFc7OEdextDj7td2vOEPJYXeO98omov11ogHn1NAiQ+oiAVqmbeba0a1cv8GJZ+ReiCdeFzyQx+4c2SPLXHMC0ov8pSwSIVcmWrPNzgkIvIjOK+Z+hBx259hmk0W0U5OEHFkvPC+VGieeC+5jhBgWnn8LSSKq8I6MTSBZaiScpfTflVR0S5YZI8+Xgkc3H6XfOSWJ6KAmiAlAnH2KPG/xBWgpHYyuw2K1lPgmFDxShOua6UxZQaRJEpFkoTmByAKhlC6tr6T9NSLaojs7Mp9ddYa+9c2BqbMrfBDF/Bij+O5sSSAwjbS5KJO/WyOiLboz+Z/YR9cZ+nbeM/edmr5/mtvyY+9RbHemHRX6+B0+GpfqoRQRvbs706INdZvSscXqoZiNa0RUfHc2J6I9bouStC8R2xPOWikiejdzImpwdvdMg2fP8lb1yqOAV7NaRDoFn3DOqnAikfMiicj+OmKLlCQi8HYN+AwmgdPig2dQv89lGBHm2gPPLalI3BrFWbd7rDhs5LEFShNRx73durvSflkSEPirodJomNo6srJQ3+GyT8d9wfjopWtpIgJnU6yekjrtEXukhiqtvZeL5pw3AEmUKKIcVDjbv+kkfzN+VURHyqyDPpJfFFFPWEA7nmvzjSu/JqJYp9pGfjcW0EcBv5DaQ52dHqVfxr4d3eHoE9RvTedyjjY3DMMwDMMwDMMwDMMwPp1/BgCgoCGZtUIAAAAASUVORK5CYII=\" alt=\"a1 = a2 = 1\" style=\"width: 72.5px; height: 20px;\" width=\"72.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.79167px; transform-origin: 15.5583px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ0AAAAoCAYAAADkBK85AAAFqElEQVR4nO2cYZWrMBCFrwccYKAGUFAFdYCDOngWqqES1kMtrIZa2PcD7sk0TUIICSTtfOfkxyu0GybDZTIzPEBRFEVRFEXZlx7Av6MnoSgHcAZwOXoSLXIF8Hf0JBTlAH7moaxERUP5VlQ0ElHRUL4VFY1E1ojGCcA4f+cKYCg1KUXZARWNRGJEo8dk3D/HeGASE0VpDRWNRJZEowPwhBGIHwC/eBWOX6hwKO2hopHIkmjcMYmGLQoDJhGhcNyLzK59hnl0R09EeUNFI5GQaPTzMV8UweN/mIRFb4x3aB+NxOpDRSORkGhcsdz4dYfeGCHUNvWiopFISDQumKKJmO/rjeFGbVMvWUVDlhZZVhzmf3/a4m/t0+D3n5Hn95jE6ArTwkt7nzfMo1b2EI1v8lebEya/kb7TwfhYyKeyiMYJpjowYjL8Da8Jv6Un71p6mL6HLSO1Z2KraHB7srSN6TDZ8jmfO2CysbTtJ74HUFI0jvDXGhjx3gJA3znDVPs4fMKxWTQuMOVDO6EnS4u5GfB6galjTPz7W0WDCxRyztN83hPv4iYX/xMdvJRoHOWvNUFxZBL+gumaB0xCQTv4HmibRCO0AIj441vIFWmkOuUW0aDdroFzQoIBGNF4JM6hdkqIxpH+WhPsF7pj8i1pD/kw9kXhyaIhFcn14/3C8dZJFY0O0yL9wF9q7WEiEZ+w/C4crx3unX1D3sCh82L5dn8l8jpHmAiDyFybzz+TREN2O/qak6jqn9qHkCoaN/ifdIRRhC9JWouDy0Ti2ryKr71+zYhNIrforxeUyefwOhlx2dtz5tpCTYdJohFTLqRTfGo9N0U0LpicMpSDkOGhL98S8zQoDZOz8uZf8z5NbKRxC5wTm49qyV9lx7CdiNwisBR12R/kutaYXF+SaFC1fV+Ujl8qfG6tehIjGIBZVJ8gyKfmUQ5+xeuTqINx9FxzypnTqMFfY2D5nFtPuxy6xc/pd7SF7xWHmOT6atGIMbB8+pSqd7dUPYkVDIh5+RZFPjVT576VB96v5QQzrxzRTy7/qcVf18D55O6/kba4OY7/g9m2hFgtGtJpXRc14lXNSoXPrVRPBiwLBhu35KK6MvisqBydz/A5c42iUYu/rqGUaFAUfHZltEjf8/lsVtFgvZchNn+Y+1LCbjTusygALTUpxYgGb/LQ4jO0PyMsGidMtr3h1cEveF3AHqarkb8/zqP0DcG8Rq7fKi0atfprKdGgKLgiCTu53s3zcNl/tWjIMJRlQ+63WBWgct/mIfe/PI/hNZ2ePQmtNCotiYbss/gJjCdeF5G2k//Xhmy+uYvj/LwT59Hh7vP3H/An1nJCwcu1ZcolGi36awnR6BDepo3ieI/JZ3yimJQIlRlYjjuM8z6tz23oxCPME5WG+gTRsLcRS0Mu4ug4LqsS0vau0i1D0CvMwnKuJSO5G/I2muXMMbTmryVEQ5ZaXdtaeXxJ/Dc1d7HsZRsu9NIPFY8NTiRnaLsHIdFYKifaw77xT+KYbUOGxj6HooM/xO/SCeXf4RqlztGerysbv4Xcick9/DWXTUuIhpybD/bcLAnh7q/GS0Xj5BjattS+u7bkugdyXyqjCpeDM8yOHT4H5943d1K2lv+5a42/5rJpqZxGLnYXDSbyZMmHN2CtRnJRo2jIdytIaUG+47jS7x4c4a8qGhZMKskQiEZqiRpFgw4uowzOs0R59ga3YJxxfISQiyP8VUVDwPBZhsrcMzLEdTWd1EiNokEHlzfsQ3yWM2dkVxnI4Pm8RY7yVxUNAcNnmYxh+Lx7yLMRviFYC3Rw24bcrsjE6FZcFR45Wuq3CXGEv8oScK3bvjt2fLgzg207L5uPWqJDXeVhVlzsCoDP5qnEvAPxKeztr7JqxlHjVq9HfXNSFEVRFEVRFEVRFEVRFEVRFEVRFEX5FP4DublNQJId8NIAAAAASUVORK5CYII=\" alt=\"a_n = |2 a_{n-2} + a_{n-1} – n|\" style=\"width: 134.5px; height: 20px;\" width=\"134.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 7.79167px; transform-origin: 12.05px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n \u003e 2\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.65px 7.79167px; transform-origin: 383.65px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAmong the Z-sequence’s properties, the magazine staff pointed out that “successive values seem unpredictable; that is, the values jump around, but not too wildly” and “almost every integer appears as a term in the sequence sooner or later, except for a few numbers, such as 245, 449, 569, 575, and 903.”\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 178.775px 7.79167px; transform-origin: 178.775px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find the index of the first occurrence of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129.925px 7.79167px; transform-origin: 129.925px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (including the five numbers above) in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.8583px 7.79167px; transform-origin: 61.8583px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ePopular Computing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8417px 7.79167px; transform-origin: 40.8417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eZ-sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = findInPopCompZ(k)\r\n  y = f(k);\r\nend","test_suite":"%%\r\nassert(isequal(findInPopCompZ(1),1))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(2),4))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(4),35))\r\n    \r\n%%\r\nassert(isequal(findInPopCompZ(19),282))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(29),30))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(49),1398))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(211),241))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(245),11309))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(348),372))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(449),13409))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(569),19434))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(575),22350))\r\n    \r\n%%\r\nassert(isequal(findInPopCompZ(903),18057))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(3347),74105))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(3491),128405))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(3690),4083))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(4250),199563))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(7431),8346))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(7488),299263))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(9735),390685))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(9792),391799))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(9851),1562345))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(findInPopCompZ(4474)),15458))\r\n\r\n%%\r\nfiletext = fileread('findInPopCompZ.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-11T03:26:33.000Z","updated_at":"2026-01-14T15:14:04.000Z","published_at":"2021-07-11T03:30:22.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere’s a quick one. In 1977 the magazine \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePopular Computing\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sought “problem situations for which the computer is the best (if not the only) tool for solution” and proposed the Z-sequence as a candidate “problem situation:”\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a1 = a2 = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_1 = a_2 = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a_n = |2 a_{n-2} + a_{n-1} – n|\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_n = |2 a_{n-2} + a_{n-1} – n|\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n \u0026gt; 2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \u0026gt; 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAmong the Z-sequence’s properties, the magazine staff pointed out that “successive values seem unpredictable; that is, the values jump around, but not too wildly” and “almost every integer appears as a term in the sequence sooner or later, except for a few numbers, such as 245, 449, 569, 575, and 903.”\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find the index of the first occurrence of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (including the five numbers above) in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePopular Computing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eZ-sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55275,"title":"List the semiprimes","description":"A semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers  and  are semiprimes, but  and  are not. The semiprimes appear in three of Ramon Villamangca’s “Easy Sequences”: Cody Problems 52859, 52990, and 53740. \r\nWrite a function to list the semiprime numbers less than or equal to the input number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 297.167px 8px; transform-origin: 297.167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"6 = 2x3\" style=\"width: 60.5px; height: 18px;\" width=\"60.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"9 = 3x3\" style=\"width: 60.5px; height: 18px;\" width=\"60.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are semiprimes, but \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"8 = 2x2x2\" style=\"width: 84px; height: 18px;\" width=\"84\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"30 = 2x3x5\" style=\"width: 91.5px; height: 18px;\" width=\"91.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 205.517px 8px; transform-origin: 205.517px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are not. The semiprimes appear in three of Ramon Villamangca’s “Easy Sequences”: Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52859\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e52859\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52990\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e52990\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53740\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e53740\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.75px 8px; transform-origin: 264.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the semiprime numbers less than or equal to the input number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = semiprimes(n)\r\n  s = primes(n)/2;\r\nend","test_suite":"%%\r\nn = 100; \r\ns = semiprimes(n);\r\ns_correct = [4 6 9 10 14 15 21 22 25 26 33 34 35 38 39 46 49 51 55 57 58 62 65 69 74 77 82 85 86 87 91 93 94 95];\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\nn = 1000; \r\ns = semiprimes(n);\r\ns_correct = [4 6 9 10 14 15 21 22 25 26 33 34 35 38 39 46 49 51 55 57 58 62 65 69 74 77 82 85 86 87 91 93 94 95 106 111 115 118 119 121 122 123 129 133 134 141 142 143 145 146 155 158 159 161 166 169 177 178 183 185 187 194 201 202 203 205 206 209 213 214 215 217 218 219 221 226 235 237 247 249 253 254 259 262 265 267 274 278 287 289 291 295 298 299 301 302 303 305 309 314 319 321 323 326 327 329 334 335 339 341 346 355 358 361 362 365 371 377 381 382 386 391 393 394 395 398 403 407 411 413 415 417 422 427 437 445 446 447 451 453 454 458 466 469 471 473 478 481 482 485 489 493 497 501 502 505 511 514 515 517 519 526 527 529 533 535 537 538 542 543 545 551 553 554 559 562 565 566 573 579 581 583 586 589 591 597 611 614 622 623 626 629 633 634 635 649 655 662 667 669 671 674 679 681 685 687 689 694 695 697 698 699 703 706 707 713 717 718 721 723 731 734 737 745 746 749 753 755 758 763 766 767 771 778 779 781 785 789 791 793 794 799 802 803 807 813 815 817 818 831 835 838 841 842 843 849 851 862 865 866 869 871 878 879 886 889 893 895 898 899 901 905 913 914 917 921 922 923 926 933 934 939 943 949 951 955 958 959 961 965 973 974 979 982 985 989 993 995 998];\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\nn = 10000; \r\ns = semiprimes(n);\r\nlen_correct = 2625;\r\nsum_correct = 12736914;\r\nvar_correct = 8.447173943104530e+06;\r\nassert(isequal(length(s),len_correct) \u0026\u0026 isequal(sum(s),sum_correct) \u0026\u0026 abs(var(s)-var_correct)\u003c1e-8)\r\n\r\n%%\r\nn = 100000; \r\ns = semiprimes(n);\r\nlen_correct = 23378;\r\nsum_correct = 1138479765;\r\nvar_correct = 8.471797671132822e+08;\r\nassert(isequal(length(s),len_correct) \u0026\u0026 isequal(sum(s),sum_correct) \u0026\u0026 abs(var(s)-var_correct)\u003c1e-6)\r\n\r\n%%\r\nn = 800000; \r\ns = semiprimes(n);\r\nlen_correct = 169660;\r\nsum_correct = 66262251604;\r\nvar_correct = 5.417425253731966e+10;\r\nassert(isequal(length(s),len_correct) \u0026\u0026 isequal(sum(s),sum_correct) \u0026\u0026 abs(var(s)-var_correct)\u003c1e-4)\r\n\r\n%%\r\nfiletext = fileread('semiprimes.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-08-02T01:42:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-02T01:34:03.000Z","updated_at":"2025-08-03T17:11:25.000Z","published_at":"2022-08-02T01:42:35.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"6 = 2x3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6 = 2\\\\times 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"9 = 3x3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e9 = 3 \\\\times 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are semiprimes, but \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"8 = 2x2x2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e8 = 2\\\\times2 \\\\times 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"30 = 2x3x5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e30 = 2\\\\times 3 \\\\times 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are not. The semiprimes appear in three of Ramon Villamangca’s “Easy Sequences”: Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52859\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e52859\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52990\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e52990\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53740\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e53740\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list the semiprime numbers less than or equal to the input number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42647,"title":"Recursion - Fun","description":" Generate the first k terms in the sequence a(n) define recursively by \r\n\r\n a(n+1)=p*a(n)+(1+a(n)) with p=0.9 and a(1)=0.5\r\n\r\nTest Case\r\n\r\n    n = 2;\r\n    a = [a(1) a(2)] = [0.5000    1.9500]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 163.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 81.7333px; transform-origin: 407px 81.7333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 81.7333px; transform-origin: 404px 81.7333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 284px 8.5px; tab-size: 4; transform-origin: 284px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 40px 8.5px; transform-origin: 40px 8.5px; \"\u003e Generate \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 244px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 244px 8.5px; \"\u003ethe first k terms in the sequence a(n) define recursively by \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 188px 8.5px; tab-size: 4; transform-origin: 188px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 116px 8.5px; transform-origin: 116px 8.5px; \"\u003e a(n+1)=p*a(n)+(1+a(n)) with \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 72px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 72px 8.5px; \"\u003ep=0.9 and a(1)=0.5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 20px 8.5px; transform-origin: 20px 8.5px; \"\u003eTest \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 16px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 16px 8.5px; \"\u003eCase\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 40px 8.5px; tab-size: 4; transform-origin: 40px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    n = 2;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 160px 8.5px; tab-size: 4; transform-origin: 160px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    a = [a(1) a(2)] = [0.5000    1.9500]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function out = rec_fun(x)\r\n  p = 0.9;\r\n  out(1) = 0.5;\r\nend","test_suite":"%%)\r\nx = 1;\r\ny_correct = 0.5;\r\nassert(abs(rec_fun(x) - y_correct) \u003c 1e-4)\r\n\r\n%%\r\nx = 5;\r\ny_correct = [0.5000    1.9500    4.7050    9.9395   19.8851];\r\nassert(sum(abs(rec_fun(x) - y_correct)) \u003c 1e-4)\r\n\r\n%%\r\nx = 7;\r\ny_correct = [0.5000    1.9500    4.7050    9.9395   19.8851   38.7816   74.6850];\r\nassert(sum(abs(rec_fun(x) - y_correct)) \u003c 1e-4)\r\n\r\n%%\r\nx = 9;\r\ny_correct = [0.5000    1.9500    4.7050    9.9395   19.8851   38.7816   74.6850 142.9016  272.5130];\r\nassert(all(abs(rec_fun(x) - y_correct) \u003c 1e-4))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":7,"created_by":44015,"edited_by":223089,"edited_at":"2023-03-07T10:35:00.000Z","deleted_by":null,"deleted_at":null,"solvers_count":45,"test_suite_updated_at":"2023-03-07T10:33:48.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-10-03T06:35:03.000Z","updated_at":"2025-12-12T06:32:21.000Z","published_at":"2015-10-03T06:36:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Generate the first k terms in the sequence a(n) define recursively by \\n\\n a(n+1)=p*a(n)+(1+a(n)) with p=0.9 and a(1)=0.5\\n\\nTest Case\\n\\n    n = 2;\\n    a = [a(1) a(2)] = [0.5000    1.9500]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"sequence\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"sequence\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"sequence\"","","\"","sequence","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f19421ecd20\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f19421ecc80\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f19421ec3c0\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f19421ecfa0\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f19421ecf00\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f19421ece60\u003e":"map(difficulty_value,0,0,999) 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v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"tag:\"sequence\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"sequence\"","","\"","sequence","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f19421ecd20\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f19421ecc80\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f19421ec3c0\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f19421ecfa0\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f19421ecf00\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f19421ece60\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f19421ecdc0\u003e":"tag:\"sequence\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f19421ecdc0\u003e":"tag:\"sequence\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":1506,"difficulty_rating":"easy"},{"id":42715,"difficulty_rating":"easy"},{"id":60286,"difficulty_rating":"easy"},{"id":1655,"difficulty_rating":"easy"},{"id":44818,"difficulty_rating":"easy"},{"id":48005,"difficulty_rating":"easy"},{"id":61168,"difficulty_rating":"easy"},{"id":44225,"difficulty_rating":"easy"},{"id":42833,"difficulty_rating":"easy"},{"id":48030,"difficulty_rating":"easy"},{"id":43684,"difficulty_rating":"easy"},{"id":48065,"difficulty_rating":"easy"},{"id":54770,"difficulty_rating":"easy"},{"id":54675,"difficulty_rating":"easy"},{"id":48020,"difficulty_rating":"easy"},{"id":47255,"difficulty_rating":"easy"},{"id":45254,"difficulty_rating":"easy"},{"id":60306,"difficulty_rating":"easy"},{"id":44543,"difficulty_rating":"easy"},{"id":60271,"difficulty_rating":"easy"},{"id":42835,"difficulty_rating":"easy"},{"id":45224,"difficulty_rating":"easy"},{"id":3011,"difficulty_rating":"easy"},{"id":59791,"difficulty_rating":"easy"},{"id":47265,"difficulty_rating":"easy"},{"id":57869,"difficulty_rating":"easy"},{"id":47239,"difficulty_rating":"easy"},{"id":60276,"difficulty_rating":"easy"},{"id":50953,"difficulty_rating":"easy"},{"id":56240,"difficulty_rating":"easy"},{"id":47310,"difficulty_rating":"easy-medium"},{"id":3010,"difficulty_rating":"easy-medium"},{"id":45384,"difficulty_rating":"easy-medium"},{"id":44544,"difficulty_rating":"easy-medium"},{"id":45253,"difficulty_rating":"easy-medium"},{"id":51002,"difficulty_rating":"easy-medium"},{"id":51820,"difficulty_rating":"easy-medium"},{"id":42836,"difficulty_rating":"easy-medium"},{"id":61052,"difficulty_rating":"easy-medium"},{"id":47295,"difficulty_rating":"easy-medium"},{"id":51274,"difficulty_rating":"easy-medium"},{"id":47370,"difficulty_rating":"easy-medium"},{"id":47345,"difficulty_rating":"easy-medium"},{"id":56593,"difficulty_rating":"easy-medium"},{"id":60266,"difficulty_rating":"easy-medium"},{"id":50913,"difficulty_rating":"easy-medium"},{"id":48025,"difficulty_rating":"easy-medium"},{"id":52283,"difficulty_rating":"easy-medium"},{"id":55275,"difficulty_rating":"easy-medium"},{"id":42647,"difficulty_rating":"easy-medium"}]}}