I voted to close this question about a "5n+1" version of the Collatz conjecture because it appears to be entirely unmotivated, with no heuristics and not even any substantial numerical evidence.

I don't see the difference in principle between this question and "How many solutions are there to this diophantine equation I've just randomly typed?".

On the other hand, I can imagine this question generating some interesting answers (e.g. applying ideas from Conway's argument that Collatz-like problems are in general undecideable). So I'm opening this thread in case others want to comment.

massivelyupvoted answer). $\endgroup$