Eventually getting to a power of 2 means that n*3 must eventually, at some point, be a non-prime Mersenne number. If there were something about the initial cond

Eventually getting to a power of 2 means that n*3 must eventually, at some point, be a non-prime Mersenne number. If there were something about the initial conditions it feels like you'd be saying something about the distribution of Mersenne primes, which is unlikely?