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%I #8 Mar 18 2022 13:15:15
%S 5,5,7,5,11,13,5,17,13,5,19,17,29,5,23,31,29,19,29,41,37,17,37,43,53,
%T 41,37,29,53,59,53,61,53,41,67,59,47,71,5,47,29,79,71,73,83,53,83,37,
%U 59,83,37,29,71,29,101,103,107,67,89,73,67,59,101,79,59,107,79,113,5,109
%N Largest prime "r" 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 See A352240.
%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) - A352443(n).
%e a(12) = 17; 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 "r" among the Goldbach pairs is 17.
%Y Cf. A187797, A278700, A352240, A352248, A352283.
%Y Cf. A352443, A352444, A352445.
%K nonn
%O 1,1
%A _Wesley Ivan Hurt_, Mar 16 2022
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