Pick a positive integer to start a sequence. Now double it, and add one to the result: this is the second number of your sequence. Double that number, and add one, and that will be your third number; repeat the doubling and adding, and you will have a fourth number, and so on.

If you start with a prime number, and you keep doubling and adding one, is it possible to produce a sequence with only prime numbers?

(In reply to I would take that bet by Gamer)

1. The starting number is to be a PRIME (by the last sentence of the problem statement).

2. It appears that Bernie Hunt's comment proves FK's conjecture, so it looks like you lose!

3.  Another conjecture to work on is: Among the first 7 terms, at least one is divisible by 3, 5, or 7.

Posted by Richard on 2006-11-29 21:28:19