It would be nice to have a more precise definition.
Table of n, a(n) for n=0..30.
Jonas Kaiser, On the relationship between the Collatz conjecture and Mersenne prime numbers, arXiv preprint arXiv:1608.00862 [math.GM], 2016. See Table 1.
Sequence in context: A063601 A222604 A112809 * A237043 A243905 A062017
Adjacent sequences: A289656 A289657 A289658 * A289660 A289661 A289662
N. J. A. Sloane, Jul 24 2017