A352351 Primes "p" 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.

3, 3, 5, 3, 3, 11, 3, 3, 23, 13, 31, 31, 47, 61, 3, 23, 31, 53, 31, 61, 61, 73, 73, 3, 83, 3, 23, 31, 151, 61, 83, 73, 31, 131, 23, 131, 131, 61, 131, 31, 199, 151, 61, 73, 73, 3, 31, 151, 157, 61, 73, 251, 151, 157, 3, 31, 131, 23, 151, 157

Offset: 1

Author

Wesley Ivan Hurt, Mar 12 2022

Keywords

• nonn

Comments

See A352297.

Examples

			a(9) = 23; 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 "p" in the definition is 23.
		

Links

• Eric Weisstein's World of Mathematics, Goldbach Partition
• Wikipedia, Goldbach's conjecture
• Index entries for sequences related to Goldbach conjecture
• Index entries for sequences related to partitions

Crossrefs

Cf. A352297, A352248, A352283, A352240.

Cf. A352352 (for primes "q"), A352353 (for primes "r"), A352354 (for primes "s").

Formula

a(n) = A352297(n) - A352352(n).