[Retric]

In theory this will eventually overflow even with pythons Arbitrary precision due to the machines finite memory. Though for practical cases it's going to run until the machine encounters an error.

If your asking the underlying math problem, yes that is true for all positive integers. It's much more obvious in base 3.

[darkmighty]

Sorry, I probably failed at writing a simple Collatz conjecture search (it should halt if Collatz is false).

https://en.wikipedia.org/wiki/Collatz_conjecture