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

1,1

Comments

See A352297.

Links

Table of n, a(n) for n=1..60.

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

Formula

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

Example

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.

Crossrefs

Cf. A352297, A352248, A352283, A352240.

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

Sequence in context: A162277 A365512 A060397 * A359421 A014780 A216199

Adjacent sequences: A352348 A352349 A352350 * A352352 A352353 A352354

Keyword

nonn

Author

Wesley Ivan Hurt, Mar 12 2022

Status

approved