Project Euler Collatz

Collatz Problem

The following iterative sequence is defined for the set of positive integers:

• n → n/2 (n is even)
• n → 3n + 1 (n is odd)

Using the rule above and starting with 13, we generate the following sequence:

13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1

It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.

Instructions

• Write a method even_next(n) that returns the next value in the sequence for an even input n
• Write a method odd_next(n) that returns the next value in the sequence for an odd input n
• Write a method next_value(n) that returns the next value in the sequence for any (integer) input n
• Write a method collatz(n) that returns the Collatz sequence from n to 1, in an array
• Write a method longest_collatz that returns the starting number under one million that returns the longest sequence
• Run learn until you get all of the RSpec tests to pass.

Source

• Project Euler - Problem 14

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