A352354 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.

5, 11, 11, 17, 29, 29, 41, 59, 53, 79, 61, 73, 83, 73, 149, 131, 151, 131, 157, 151, 157, 151, 157, 239, 167, 269, 251, 271, 157, 271, 251, 271, 331, 233, 353, 251, 257, 331, 263, 367, 211, 271, 373, 367, 373, 461, 433, 331, 331, 433, 433, 257, 367, 373, 569, 541, 443, 557, 433, 433

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) - A352353(n).

Example

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.

Crossrefs

Cf. A352297, A352248, A352283, A352240.

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

Sequence in context: A352443 A181667 A060846 * A113002 A179618 A058197

Adjacent sequences: A352351 A352352 A352353 * A352355 A352356 A352357

Keyword

nonn

Author

Wesley Ivan Hurt, Mar 12 2022

Status

approved