Just a little observation, this appears to be a baby version of the unsolved **3n+1 problem**, whose conjectured answer is known as the Collatz Conjecture.

The only difference is that for odd numbers `n`

you replace with `3n+1`

. It's conjectured that you can always get to 1 by following the rules, but to this day it remains unproved.

Fortunately this one is much easier. :)