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 A bet by Federico Kereki)

As far as term N being divisible by T (the first term), that is sometimes true but not always true.

Consider T=9: 9, 19, 39, 79, 159, 319, 639, 1279, 2559, ...

The ninth term is not divisible by 9. (Instead, the seventh term is)

This is because the other numbers (besides T-1) don't form one complete cycle. 2 and 5 are absent because 2*1+1=0*9+5 and 2*5+1=1*9+2, thus forming their own cycle.

Posted by Gamer on 2006-11-29 20:44:10