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)
This conjecture is true for all primes through 8647. The verification program crashes with an overflow on the 8659th iteration of the doubling and adding for the next prime, 8663.
20 while Ct<48
40 for I=1 to N-1
70 if Nu @ N>0 then print N,Nu:Ct=Ct+1
Overflow in 50
Line 70 would have shown any exception to the rule.
Posted by Charlie
on 2006-11-30 09:07:59