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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?

 May 22, 2020
 #1
avatar+744 
-1

this is clearly an AoPS question.

 May 22, 2020
 #2
avatar+744 
-1

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)).

 May 22, 2020
 #3
avatar+30926 
+2

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.

 May 22, 2020
 #4
avatar+744 
0

I think you're right, Alan!

 May 22, 2020

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