/sci/ - Science & Math

Hello. I remember you posting about Collatz on /pol/ a while ago. Interesting problem. Thank you for introducing it to me.
>>10631620
is a quality post.

Perhaps you can tell me if there is any work analyzing the problem from the perspective of prime factorization. I'm thinking about a number in the form of something like 2x3^2x5x7. Then the Collatz rules read something like "If there is a 2, remove it. If there is no 2, multiply by 3 and add 1" the latter being the interesting part because it "converts" in a likely predictable way prime factors into another configuration (guaranteed to contain a 2). The branch diagram here helps a lot to illustrate this.

TL;DR - Does anybody think about Collatz as a 'converter-elimination engine' operating on prime factorizations, converting every prime number that isn't 2 into 2 for elimination? I will be thinking about what effect the 3n + 1 operator could be said to have exactly.