Can someone explain to me what is so amazing about the question that collatz is asking? It's a pretty simple concept in my mind, I guess the first way I "boxed it up" was HoTPO in its simplest cycle is 4,2,1 and asking the same questions from any higher integers is purely an offset, the integer I start with is my coefficient and the instructions are built in to factor it out. We also have a bit of logic in it, if even then divide, if odd then multiply and add 1, the answer is in the question

HALF or Triple Plus 1 2=half 4=triple+1 it's just factored to smallest terms, yeah it climbs up and down before it's all factored out but that's the nature of climbing on odds and falling on evens but there's more evens because the equation asks for evens thus it eventually falls all the way to simplest terms 4,2,1

is there something greater to this numerical oddity?

is it because it's easy credit?