Problem 43649. 4 Digit Sequence Repetitions

Given a 4 digit integer, a sequence can be created such that the next digit in the sequence is the ones digit from the sum of the four immediately preceding digits.

For example, the first four terms of our infinite sequence of decimal digits are 2, 0, 0, 9. Thus our sequence begins:

2, 0, 0, 9, 1, 0, 0, 0, 1, 1, 2, 4, 8, 5, 9, 6, 8, 8, 1, 3, 0, 2, 6, 1, 9, 8, 4, 2, 3, 7, ...

Given a seed sequence and another 4 digit test pattern, determine the index for the test pattern following the seed sequence, if it exists. Return the index of the first occurrence of the test pattern. If the pattern does not appear, return 0.

For example, in the above sequence, [2 0 0 9] is the seed sequence and if [1 0 0 0] is the test sequence, it has index 5.

Taken from L-S Hahn's New Year's Puzzle for 2009