A279792 Number of Goldbach partitions (p,q) of 2n such that 0 < |p-q| < n.

0, 0, 0, 1, 1, 1, 0, 1, 2, 1, 0, 2, 1, 1, 2, 1, 1, 2, 0, 2, 3, 1, 1, 2, 2, 1, 2, 1, 1, 4, 1, 2, 3, 1, 2, 3, 1, 2, 2, 1, 2, 4, 0, 2, 5, 1, 1, 3, 2, 3, 4, 3, 1, 4, 3, 3, 5, 2, 1, 6, 1, 2, 5, 1, 3, 4, 2, 2, 4, 4, 3, 6, 3, 3, 7, 2, 4, 6, 1, 4, 5, 2, 2, 5, 4, 3, 5, 3, 2, 6

Offset: 1

Author

Wesley Ivan Hurt, Dec 18 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. A010051, A002375, A279794.

Programs

Maple

with(numtheory): A279792:=n->add( (pi(i)-pi(i-1)) * (pi(2*n-i)-pi(2*n-i-1)) * signum(floor(n/(2*(n-i)))), i=3..n-1): seq(A279792(n), n=1..100);

Mathematica

Table[Sum[Boole[PrimeQ@ i] Boole[PrimeQ[2 n - i]] Sign@ Floor[n/(2 (n - i))], {i, 3, n - 1}], {n, 90}] (* Michael De Vlieger, Dec 21 2016 *)

Formula

a(n) = Sum_{i=3..n-1} A010051(i) * A010051(2n-i) * sign(floor(n/(2*(n-i)))).