A279103 Number of Goldbach partitions (p,q) of 2n such that there exists a prime r in p < r < q that does not appear as a part in any Goldbach partition of p+q = 2n.

0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 0, 2, 2, 0, 2, 3, 2, 1, 3, 3, 3, 3, 5, 4, 2, 5, 3, 3, 1, 2, 5, 6, 1, 5, 6, 4, 5, 6, 4, 4, 5, 4, 4, 8, 4, 4, 7, 3, 5, 8, 5, 4, 8, 6, 6, 10, 6, 5, 10, 3, 5, 10, 2, 7, 9, 5, 5, 7, 7, 7, 10, 5, 5, 12, 3, 8, 11, 4, 8, 8, 5, 5, 13, 9, 5, 11, 7

Offset: 1

Author

Wesley Ivan Hurt, Dec 06 2016

Keywords

• nonn
• easy

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. A002375, A010051, A278700.

Formula

a(n) = A002375(n) - A278700(n).

a(n) = Sum_{i=3..n} (A010051(i) * A010051(2n-i) * (1 - Product_{k=i..n} (1 - abs(A010051(k) - A010051(2n-k))))).