Sequence Question
(In the spirit of the 3N+1 sequence question...)
Start with any positive integer N.
If N is prime (or 1) replace it with 2N+1.
If N is composite, replace it with its largest prime factor.
Repeat these steps.
For example, if N=3 we get the cycle
3 > 7 > 15 > 5 > 11 > 23 > 47 > 95 > 19 > 39 > 13 > 27 > 3.
The question is: does every N eventually evolve into this cycle?
