Problem 14 of the Euler Project is about the Collatz sequence. Officially it is a conjecture that every sequence starting with n ends in 1.
I spend so much time on 3x+1.... My first blog post in 2005 was on the Collatz sequence. I am able to generate sequences of any length ( thus including very large lengths ) but they end with 1 by definition. It's sort of a paradox.