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%I #8 Mar 18 2022 19:04:21
%S 3,3,5,3,5,7,3,5,11,3,5,7,13,3,5,11,3,5,23,11,7,13,31,19,3,5,31,3,5,7,
%T 13,19,47,7,61,3,5,11,3,5,23,11,17,7,13,3,5,31,53,11,31,3,5,3,5,11,17,
%U 61,47,29,61,47,29,73,3,5,73,7,3,5,11,83,17,23,37,29,3,5,23
%N Smallest prime "p" among all pairs of Goldbach partitions of A352240(n), (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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = A352240(n) - A352444(n).
%e a(12) = 7; A352240(12) = 54 has 3 pairs of Goldbach partitions (7,47),(11,43); (11,43),(13,41); and (13,41),(17,37); with all integers composite in the open intervals (7,11) and (43,47), (11,13) and (41,43), and, (13,17) and (37,41) respectively. The smallest prime "p" among all Goldbach pairs is 7.
%Y Cf. A187797, A278700, A352240, A352248, A352283.
%Y Cf. A352442, A352443, A352444.
%K nonn
%O 1,1
%A _Wesley Ivan Hurt_, Mar 16 2022
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