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A352444 Largest prime "q" 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 A352444 #7 Feb 16 2025 08:34:03
%S A352444 7,13,13,19,19,23,31,31,31,43,43,47,47,61,61,61,73,73,59,73,83,83,67,
%T A352444 83,103,103,79,109,109,113,113,113,89,131,79,139,139,139,151,151,137,
%U A352444 151,151,167,167,181,181,157,137,181,163,193,193,199,199,199,199,157,173,193,163
%N A352444 Largest prime "q" 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 A352444 See A352240.
%H A352444 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A352444 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A352444 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A352444 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A352444 a(n) = A352240(n) - A352445(n).
%e A352444 a(12) = 47; 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 largest prime "q" among all Goldbach pairs is 47.
%Y A352444 Cf. A187797, A278700, A352240, A352248, A352283.
%Y A352444 Cf. A352442, A352443, A352445.
%K A352444 nonn
%O A352444 1,1
%A A352444 _Wesley Ivan Hurt_, Mar 16 2022