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A352351 Primes "p" 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 A352351 #15 Feb 16 2025 08:34:03
%S A352351 3,3,5,3,3,11,3,3,23,13,31,31,47,61,3,23,31,53,31,61,61,73,73,3,83,3,
%T A352351 23,31,151,61,83,73,31,131,23,131,131,61,131,31,199,151,61,73,73,3,31,
%U A352351 151,157,61,73,251,151,157,3,31,131,23,151,157
%N A352351 Primes "p" 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 A352351 See A352297.
%H A352351 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A352351 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A352351 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A352351 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A352351 a(n) = A352297(n) - A352352(n).
%e A352351 a(9) = 23; 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 "p" in the definition is 23.
%Y A352351 Cf. A352297, A352248, A352283, A352240.
%Y A352351 Cf. A352352 (for primes "q"), A352353 (for primes "r"), A352354 (for primes "s").
%K A352351 nonn
%O A352351 1,1
%A A352351 _Wesley Ivan Hurt_, Mar 12 2022