A conjecture I can't remember...

[nolispe]

There's a mathematical conjecture that I vaugely remember, but don't know the name of or the precise formulation of. It involves doing something to numbers if even, and something else if odd, and all numbers tested so far, if this is iteratively done, will reach one.
After spending about a day trying to remember it, I have finally caved, and so I ask the playground: What conjecture am I thinking of?
Any ideas?

[tensai_oni]

The Collatz Conjecture (http://en.wikipedia.org/wiki/Collatz_conjecture)?

[nolispe]

The Collatz Conjecture (http://en.wikipedia.org/wiki/Collatz_conjecture)?

Ah, thanks! That's it!
I owe you one. Specifically, I owe you one answer to a fairly easy question at some point in the future. Hey, it might be useful... but probably not.