@vzn, so I looked into parity a bit. (I couldn't really find anything about the parity sequence, though.) And I guess I never really thought about it that much, but in binary 0 is even, 1 is odd. So then if you do modular arithmetic in binary and bring it to 1 or 0, then it is still odd or even, based on that. I'm just thinking about it.

I'll add some modular arithmetic results to my collatz conjecture code.

@heather some refs study a "parity sequence" but not sure if they name it that, named it that myself. its just the sequence of 0/1s on the trajectory LSB (least significant bit). have found various patterns there.

I think I'm finding some interesting relations here...I'll have to keep messing with the numbers with the collatz conjecture program, but the mod work has had some interesting results.