Problem 42673. Longest Collatz Sequence

Inspired by Projet Euler n°14.

The Collatz iterative sequence (See Cody problem n° 2103 and 211) 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 number given in input, produces the longest chain?

Be smart because numbers can be big...