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A352297 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 A352297 #12 Feb 16 2025 08:34:03
%S A352297 10,16,18,22,34,42,46,64,82,96,98,110,136,140,154,160,188,190,194,218,
%T A352297 224,230,236,244,256,274,280,308,314,338,340,350,368,370,382,388,394,
%U A352297 398,400,404,422,428,440,446,452,466,470,488,494,500,512,514,524,536,574,578,580,586
%N A352297 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.
%H A352297 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A352297 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A352297 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A352297 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A352297 a(n) = A352351(n) + A352352(n) = A352353(n) + A352354(n).
%e A352297 82 is in the sequence since it 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.
%Y A352297 Cf. A187797, A278700, A352248, A352283, A352240.
%Y A352297 Cf. See A352351, A352352, A352353, and A352354 for values of the corresponding primes p, q, r, and s.
%K A352297 nonn
%O A352297 1,1
%A A352297 _Wesley Ivan Hurt_, Mar 11 2022