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Primes "s" 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.
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%I #7 Mar 13 2022 00:03:55

%S 5,11,11,17,29,29,41,59,53,79,61,73,83,73,149,131,151,131,157,151,157,

%T 151,157,239,167,269,251,271,157,271,251,271,331,233,353,251,257,331,

%U 263,367,211,271,373,367,373,461,433,331,331,433,433,257,367,373,569,541,443,557,433,433

%N Primes "s" 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 See A352297.

%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) = A352297(n) - A352353(n).

%e a(9) = 53; 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 "s" in the definition is 53.

%Y Cf. A352297, A352248, A352283, A352240.

%Y Cf. A352351 (for primes "p"), A352352 (for primes "q"), A352353 (for primes "r").

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, Mar 12 2022