Collatz's Ant

I've been fiddling with the Collatz Conjecture off and on for years now. I'm convinced I found a pattern that I haven't been able to find mentioned anywhere. Granted, that could be because I lack the mathematical language needed to search for it.

First, I'm going to use an implicit even step after the odd step, as 3*odd + 1 always equals even. If you look at the path a number takes to its next lowest number, for example 5->8->4, visualize it by just looking at the even and odd steps like so: 5->10, you will see that other numbers follow a similar pattern:

9->10

13->10

17->10

What do these number have in common? They follow the pattern 5 + k(2^n) where n is the number of even steps (with the implicit even step, two in this case).

For another example, look at 7:

7->1110100

Seven even steps, so the next number will be 7 + 2^7 = 135:

135->1110100

I'd love to hear if this has been found and documented somewhere. If not, I have additional ramblings to share.

The conjecture holds up through 2^68. Can't we just call it there? Lol I'm obviously being obtuse, but really is there some reason to think there would be an exception at sufficiently large integers? It's hard to even imagine that one wouldn't.

edit: I'm in way over my head. Disregard me :)

The previous piece previous thread https://news.ycombinator.com/item?id=42479375

I love that people are working on this. It's inspiring. Thank you for posting. It's interesting if you post a comment about your process, purpose or idea - and maybe a link to code, etc (even tho it's all linked in the post, HN likes comments & discussion)

I love cellular automata projects like this.

I didnt know what i was getting into but i loved it