Sure enough, I found a starting value that results in a sequence with fewer than a third primes. Where there is one, there are bound to be an infinite number of others. Finding a sequence with no primes whatsoever might prove to be somewhat more difficult task though.
Well, actually it isn't: e.g., 29013 is a starting number with a Syracuse sequence that contains no primes. Are there finitely many or infinitely many others?
Sure enough, I found a starting value that results in a sequence with fewer than a third primes. Where there is one, there are bound to be an infinite number of others. Finding a sequence with no primes whatsoever might prove to be somewhat more difficult task though.
Well, actually it isn't: e.g., 29013 is a starting number with a Syracuse sequence that contains no primes. Are there finitely many or infinitely many others?