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A352443 Smallest prime "s" 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.

%I A352443 #8 Feb 16 2025 08:34:03
%S A352443 5,11,11,17,13,17,29,19,29,41,29,37,31,59,43,41,47,59,53,43,53,79,61,
%T A352443 59,53,67,73,83,61,61,73,71,83,97,73,83,97,79,149,109,131,83,97,101,
%U A352443 97,131,103,151,131,109,157,167,127,173,103,107,109,151,131,149,157,167,127
%N A352443 Smallest prime "s" 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.
%C A352443 See A352240.
%H A352443 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A352443 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A352443 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A352443 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A352443 a(n) = A352240(n) - A352442(n).
%e A352443 a(12) = 37; 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 "s" among all Goldbach pairs is 37.
%Y A352443 Cf. A187797, A278700, A352240, A352248, A352283.
%Y A352443 Cf. A352442, A352444, A352445.
%K A352443 nonn
%O A352443 1,1
%A A352443 _Wesley Ivan Hurt_, Mar 16 2022