A352297 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.

10, 16, 18, 22, 34, 42, 46, 64, 82, 96, 98, 110, 136, 140, 154, 160, 188, 190, 194, 218, 224, 230, 236, 244, 256, 274, 280, 308, 314, 338, 340, 350, 368, 370, 382, 388, 394, 398, 400, 404, 422, 428, 440, 446, 452, 466, 470, 488, 494, 500, 512, 514, 524, 536, 574, 578, 580, 586

Offset

1,1

Links

Table of n, a(n) for n=1..58.

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) = A352351(n) + A352352(n) = A352353(n) + A352354(n).

Example

82 is in the sequence since it 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.

Crossrefs

Cf. A187797, A278700, A352248, A352283, A352240.

Cf. See A352351, A352352, A352353, and A352354 for values of the corresponding primes p, q, r, and s.

Sequence in context: A323196 A352240 A187797 * A192221 A106695 A053747

Adjacent sequences: A352294 A352295 A352296 * A352298 A352299 A352300

Keyword

nonn

Author

Wesley Ivan Hurt, Mar 11 2022

Status

approved