Project Euler Problem 14: Longest Collatz Sequence
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.
Which starting number, under one million, produces the longest chain? Note that once the chain starts the terms are allowed to go above one million.
The Collatz sequence starting from 13 is
13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
The Collatz sequence starting from 13 is 10 items long
The longest Collatz sequence starting from under 1 million starts at 837,799 and is 524 items long