A352445 Smallest prime "p" 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.

3, 3, 5, 3, 5, 7, 3, 5, 11, 3, 5, 7, 13, 3, 5, 11, 3, 5, 23, 11, 7, 13, 31, 19, 3, 5, 31, 3, 5, 7, 13, 19, 47, 7, 61, 3, 5, 11, 3, 5, 23, 11, 17, 7, 13, 3, 5, 31, 53, 11, 31, 3, 5, 3, 5, 11, 17, 61, 47, 29, 61, 47, 29, 73, 3, 5, 73, 7, 3, 5, 11, 83, 17, 23, 37, 29, 3, 5, 23

Offset: 1

Author

Wesley Ivan Hurt, Mar 16 2022

Keywords

• nonn

Examples

			a(12) = 7; 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 "p" among all Goldbach pairs is 7.
		

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. A187797, A278700, A352240, A352248, A352283.

Cf. A352442, A352443, A352444.

Formula

a(n) = A352240(n) - A352444(n).