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A352352 Primes "q" corresponding to the even numbers with exactly 1 pair of Goldbach partitions, (p,q) and (r,s) with p,q,r,s prime and p < r <= s < q, such that all integers in the open intervals (p,r) and (s,q) are composite.

%I A352352 #9 Feb 16 2025 08:34:03
%S A352352 7,13,13,19,31,31,43,61,59,83,67,79,89,79,151,137,157,137,163,157,163,
%T A352352 157,163,241,173,271,257,277,163,277,257,277,337,239,359,257,263,337,
%U A352352 269,373,223,277,379,373,379,463,439,337,337,439,439,263,373,379,571,547,449,563,439,439
%N A352352 Primes "q" corresponding to the even numbers with exactly 1 pair of Goldbach partitions, (p,q) and (r,s) with p,q,r,s prime and p < r <= s < q, such that all integers in the open intervals (p,r) and (s,q) are composite.
%C A352352 See A352297.
%H A352352 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A352352 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A352352 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A352352 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A352352 a(n) = A352297(n) - A352351(n).
%e A352352 a(9) = 59; A352297(9) = 82 has exactly one pair of Goldbach partitions, namely (23,59) and (29,53), such that all integers in the open intervals (23,29) and (53,59) are composite. The prime corresponding to "q" in the definition is 59.
%Y A352352 Cf. A352297, A352248, A352283, A352240.
%Y A352352 Cf. A352351 (for primes "p"), A352353 (for primes "r"), A352354 (for primes "s").
%K A352352 nonn
%O A352352 1,1
%A A352352 _Wesley Ivan Hurt_, Mar 12 2022