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
re(2): One Approach (Spoiler?) by Richard)
Richard:
I like your approach just fine, since it doesn't depend on some theorem that I can't prove.
re(3): One Approach (Spoiler?)
