A352443 Smallest prime "s" among all pairs of Goldbach partitions of A352240(n), (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, 13, 17, 29, 19, 29, 41, 29, 37, 31, 59, 43, 41, 47, 59, 53, 43, 53, 79, 61, 59, 53, 67, 73, 83, 61, 61, 73, 71, 83, 97, 73, 83, 97, 79, 149, 109, 131, 83, 97, 101, 97, 131, 103, 151, 131, 109, 157, 167, 127, 173, 103, 107, 109, 151, 131, 149, 157, 167, 127

Offset

1,1

Comments

See A352240.

Links

Table of n, a(n) for n=1..63.

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) = A352240(n) - A352442(n).

Example

a(12) = 37; A352240(12) = 54 has 3 pairs of Goldbach partitions (7,47),(11,43); (11,43),(13,41); and (13,41),(17,37); with all integers composite in the open intervals (7,11) and (43,47), (11,13) and (41,43), and, (13,17) and (37,41) respectively. The smallest prime "s" among all Goldbach pairs is 37.

Crossrefs

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

Cf. A352442, A352444, A352445.

Sequence in context: A205673 A394905 A245098 * A181667 A060846 A352354

Adjacent sequences: A352440 A352441 A352442 * A352444 A352445 A352446

Keyword

nonn

Author

Wesley Ivan Hurt, Mar 16 2022

Status

approved