[seqfan] Coprime To Sums

Leroy Quet q1qq2qqq3qqqq at yahoo.com
Sun Aug 30 18:08:22 CEST 2009

I think this sequence was worth submitting during Neil's vacation.

%I A164901
%S A164901 1,2,4,7,13,19,29,37,43,53,59
%N A164901 a(1)=1, a(2) = 2. For n >=3, a(n) = the smallest integer > a(n-1) that is coprime to every sum of any two distinct earlier terms of this sequence. 
%e A164901 The first 4 terms are 1,2,4,7. The sums of every pair of distinct terms are: 1+2=3, 1+4=5, 2+4=6, 7+1=8, 7+2=9, and 7+4=11. So, we are looking for the smallest integer > 7 that is coprime to 3, 5, 6, 8, 9, and 11. This number, which is a(5), is 13. 
%Y A164901 A164902,A164903 
%K A164901 more,nonn
%O A164901 1,2

(A164902 is the sequence of positive integers that each occur at least once as a sum of any two terms of A164901. A164903 is the compliment of A164902.)

I am surprised that this sequence isn't already in the OEIS. Even though I double-checked my work, did I make a mistake?

Second, Are there any more composites in the sequence? If so, are there an infinite number of composites? If so, could someone please calculate a number of terms of the sequences where one sequence contains the primes of A164901, and the other sequence contains the composites?

Leroy Quet

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