Given stuff like arxiv.org/pdf/2107.12475.pdf on Erdős' conjecture on powers of 2, it feels like this one will be somewhere close to computer science/Halting problem issues than number theory. Who knows. This is suggested e.g. at The Busy Beaver Competition: a historical survey by Pascal Michel.
We ust use the if mod notation definition as mentioned at: math.stackexchange.com/questions/4305972/what-exactly-is-a-collatz-like-problem/4773230#4773230
Described at: arxiv.org/pdf/2107.12475.pdf where a relation to the Busy beaver scale is proven, and the intuitive relation to the Collatz conjecture described. Perhaps more directly: demonstrations.wolfram.com/CollatzSequenceComputedByATuringMachine/
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The Collatz conjecture, also known as the 3n + 1 conjecture, is a famous unsolved problem in mathematics that deals with sequences defined in a particular way. The conjecture can be described as follows: 1. Take any positive integer \( n \). 2. If \( n \) is even, divide it by 2. 3. If \( n \) is odd, multiply it by 3 and add 1.