A collection S of integers is defined by the following three rules:
(I) 2 is in S;
(II) for every x in S, 3x and x + 7 are also in S;
(III) no integers except those defined by rules (I) and (II) are in S.
What is the smallest integer greater than 2004 which is NOT in S?
fine, I'll give it a try, I think the answer is 2009, because all terms that are multiples of 7 are NOT in the list, so 2009 is the smallest multiple of 7 that is greater than 2004 (2(mod 7)).
It must be an integer that is not even and not divisible by 3. It must have a remainder of 2 when divided by 7 (because the set starts with 2);
I make 2011 the first to satisfy these conditions.