Project Euler, Problem 14: Longest Collatz Sequence

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

n \to \frac{n}{2} (n is even)

n \to 3 n + 1 (n is odd)

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

13 \to 40 \to 20 \to 10 \to 5 \to 16 \to 8 \to 4 \to 2 \to 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: Once the chain starts the terms are allowed to go above one million.

I store the lengths of the Collatz sequences in an array so I don't have to calculate the entire sequence for every number. This reduces the run time over my previous attempt by a factor of 20.

I use a while loop to run through the sequence until I reach one or a number previously in the sequence and I store the longest sequence and the number that produced it as I go along.

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