A279730 Partial sums of A279729.

0, 0, 6, 14, 34, 46, 60, 60, 96, 96, 118, 190, 216, 216, 306, 306, 340, 412, 450, 450, 492, 492, 538, 538, 538, 590, 590, 590, 648, 948, 1010, 1010, 1010, 1078, 1078, 1078, 1152, 1152, 1230, 1230, 1312, 1564, 1650, 1650, 1740, 1740, 1834, 1834, 1834, 1934

Offset

1,3

Links

Table of n, a(n) for n=1..50.

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

Maple

with(numtheory): A279730:=n->2*add(add(j * (pi(i)-pi(i-1)) * (pi(2*j-i)-pi(2*j-i-1)) * (product(1-abs((pi(k)-pi(k-1))-(pi(2*j-k)-pi(2*j-k-1))), k=i..j)), i=3..j), j=1..n): seq(A279730(n), n=1..40);

Mathematica

f[n_, x_: 0] := Sum[(If[x == 0, i, 2 n - i] Boole[PrimeQ@ i] Boole[PrimeQ[2 n - i]]) Product[1 - Abs[Boole[PrimeQ@ k] - Boole[PrimeQ[2 n - k]]], {k, i, n}], {i, 3, n}]; Accumulate@ Table[f@ n + f[n, 1], {n, 50}] (* Michael De Vlieger, Dec 18 2016 *)

Crossrefs

Cf. A278700, A279727, A279728, A279729.

Sequence in context: A142875 A074981 A066510 * A269717 A271097 A269709

Adjacent sequences: A279727 A279728 A279729 * A279731 A279732 A279733

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Dec 17 2016

Status

approved