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A352354 Primes "s" 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 A352354 #8 Feb 16 2025 08:34:03
%S A352354 5,11,11,17,29,29,41,59,53,79,61,73,83,73,149,131,151,131,157,151,157,
%T A352354 151,157,239,167,269,251,271,157,271,251,271,331,233,353,251,257,331,
%U A352354 263,367,211,271,373,367,373,461,433,331,331,433,433,257,367,373,569,541,443,557,433,433
%N A352354 Primes "s" 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 A352354 See A352297.
%H A352354 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A352354 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A352354 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A352354 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A352354 a(n) = A352297(n) - A352353(n).
%e A352354 a(9) = 53; 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 "s" in the definition is 53.
%Y A352354 Cf. A352297, A352248, A352283, A352240.
%Y A352354 Cf. A352351 (for primes "p"), A352352 (for primes "q"), A352353 (for primes "r").
%K A352354 nonn
%O A352354 1,1
%A A352354 _Wesley Ivan Hurt_, Mar 12 2022