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Be happy
check whether the given number is happy in b-base. * A happy number can be defined as a number which will yield 1 when it is ...

4 months ago

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Pell numbers
Find the nth pell number <https://en.wikipedia.org/wiki/Pell_number>

4 months ago

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love is an n-letter word
Given a list of *N words*, return the *N-letter word* (choosing one letter from each word) with the property of having the least...

4 months ago

Solved

SatCom #6: Inclination of a Sun-Synchronous Orbit
Satellite and Space Engineering - Problem #5 This is part of a series of problems looking at topics in satellite and space comm...

4 months ago

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Compute the missing quantity among P, V, T for an ideal gas
Consider 100 mol of helium gas at a certain pressure (P), volume (V), and temperature (T). Assuming that the ideal gas law appli...

4 months ago

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find the nth fibonacci number
The Fibonacci sequence is defined as follows: give n, find the nth fibonacci number

4 months ago

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find the nth number (plus)
this problem is the harder version of Problem 61014. The numbers 2 and 7 are called lucky numbers, an integer containing only t...

4 months ago

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Find nth number
The numbers 2 and 7 are called lucky numbers, an integer containing only the digits 2 and 7 is also called lucky number. The pro...

4 months ago

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Bessel Polynomials
Return the n-th Bessel polynomial Assume that n is a non-negative finite integer. bessel_poly(0) ans = 1 bessel_poly(1) ...

4 months ago

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Logistic map
The sequence defined by x_n = 4*r*x_{n-1}*(1-x_{n-1}) and a given 0 < x_1 < 1 turns each x_n into a polynomial of r. Write a fu...

4 months ago

Solved

Laguerre Polynomials
Create a square lower diagonal matrix containing the first n Laguerre Polynomial coefficients. For n=6, the Laguerre Matrix is: ...

4 months ago

Solved

ICFP2024 009: Lambdaman Crawler-Backfill
The ICFP2024 contest was held June29 thru July 1. The contest consisted of five parts: ICFP Language, Lambdaman maze, Starship f...

5 months ago

Solved

Reverse within string
If input is a string 'yellow' the output should be 'leywol'. Locate the middle of the string and reverse the first (yel) and sec...

5 months ago

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Check the integers additive decomposition conjecture
Problem statement A conjecture (I rediscovered ?) related to Goldbach's one states that every integer above 2 can be written ...

5 months ago

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Prime numbers which are the difference of two consecutive cubes
Problem statement Given a positive integer n greater than 2, find the prime numbers less or equal to n and which are the diff...

5 months ago

Solved

Barnes G-Function
Evaluate the Barnes G-Function at a given (integral) value. %Example 1 in = 1; out = 1; %Example 1 in = 4; out = 2; ...

5 months ago

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Check Legendre's conjecture
Context and problem statement Legendre's conjecture states for a given positive integer n, there always exists at least one pri...

5 months ago

Solved

Check Bertrand-Chebyshev's theorem about prime numbers
Historical context Bertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory ...

5 months ago

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Linear primes p' = mp + n
Problem statement List the prime numbers of the form p' = mp + n for a given (m,n) couple and such that p' < k, k positive in...

5 months ago

Solved

List the complementary / symetric prime couples
Problem statement For a given positive integer n, provide the prime couples (p,p') such that p + p' = 10^n. NB : a number li...

5 months ago

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List the twin prime couples
Problem statement The twin prime couples (p,p') are the ones such that p' = p + 2. For a given integer n > 1, list the twin p...

5 months ago

Solved

Check p = 6n +/- 1, the generic formula for odd prime numbers greater than 3
Problem statement For all odd prime number p greater than 3, there exists a positive integer n, such that p = 6n +/- 1 : ...

5 months ago

Solved

Check p = 4n +/- 1, the generic formula for odd prime numbers
Problem statement For all odd prime number p, there exists a positive integer n, such that p = 4n +/- 1 : Check this f...

5 months ago

Solved

Chek the Delta = p' - p = 6k gap theorem about arithmetic progressions in the prime number set
Context In the prime numbers set there are some arithmetic progressions (sequences of three or more consecutive prime number...

5 months ago

Solved

List the near-square primes, p = n² + 1 (Landau's 4th problem)
Historical context At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime...

5 months ago

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List primes which are the sum of two consecutive lower primes plus minus one
Problem statement Some prime numbers can be written as the sum of two consecutive lower primes plus / minus one : Like t...

5 months ago

Solved

Convex Hull Capture
Imagine four points in uv that form a square. uv = [ ... 0,0; 0,2; 2,2; 2,0]; Now we have two more po...

5 months ago

Solved

Minimal cost
A power house, P, is on one bank of a straight river W meters wide, and a factory, F, is on the opposite bank L meters downstrea...

5 months ago

Solved

Next Lower Power of B
Given a number _n_ and a base _B_ greater than 1, return the lowest integer power of _B_ that is less than or equal to _n_. E...

5 months ago

Solved

Find the definite integral of various linear functions
A definite integral had a minimum and maximum limit. When you solve this type of problem you must use both quad and the trapz fu...

5 months ago