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

1,8

Links

Table of n, a(n) for n=1..88.

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) = 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))))).

Crossrefs

Cf. A002375, A010051, A278700.

Sequence in context: A329491 A123063 A031358 * A318734 A029317 A127800

Adjacent sequences: A279100 A279101 A279102 * A279104 A279105 A279106

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Dec 06 2016

Status

approved