A279615 Partial sums of A279315.

0, 0, 1, 3, 7, 9, 10, 10, 16, 16, 17, 29, 30, 30, 42, 42, 43, 49, 50, 50, 52, 52, 53, 53, 53, 55, 55, 55, 56, 86, 87, 87, 87, 89, 89, 89, 90, 90, 92, 92, 93, 105, 106, 106, 108, 108, 109, 109, 109, 111, 111, 111, 115, 115, 115, 117, 117, 117, 118, 124, 125, 125, 125, 127, 127, 127, 128, 128, 130, 130, 131, 133, 134

Offset

1,4

Links

Table of n, a(n) for n=1..73.

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

Maple

with(numtheory): a:=n->add(add( (pi(i)-pi(i-1)) * (pi(2*h-i)-pi(2*h-i-1)) * (pi(2*h-i)-pi(i-1)) * (product(1-abs((pi(k)-pi(k-1))-(pi(2*h-k)-pi(2*h-k-1))), k=i..h)), i=3..h), h=1..n): seq(a(n), n=1..80);

Crossrefs

Cf. A010051, A279315.

Sequence in context: A179021 A096910 A182389 * A169968 A082768 A326911

Adjacent sequences: A279612 A279613 A279614 * A279616 A279617 A279618

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Dec 15 2016

Status

approved