cp's OEIS Frontend

A352353 Primes "r" corresponding to the 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 A352353 #9 Feb 16 2025 08:34:03
%S A352353 5,5,7,5,5,13,5,5,29,17,37,37,53,67,5,29,37,59,37,67,67,79,79,5,89,5,
%T A352353 29,37,157,67,89,79,37,137,29,137,137,67,137,37,211,157,67,79,79,5,37,
%U A352353 157,163,67,79,257,157,163,5,37,137,29,157,163
%N A352353 Primes "r" corresponding to the 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.
%C A352353 See A352297.
%H A352353 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A352353 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A352353 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A352353 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A352353 a(n) = A352297(n) - A352354(n).
%e A352353 a(9) = 29; A352297(9) = 82 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. The prime corresponding to "r" in the definition is 29.
%Y A352353 Cf. A352297, A352248, A352283, A352240.
%Y A352353 Cf. A352351 (for primes "p"), A352352 (for primes "q"), A352354 (for primes "s").
%K A352353 nonn
%O A352353 1,1
%A A352353 _Wesley Ivan Hurt_, Mar 12 2022