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A279730 Partial sums of A279729. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 12 10:52 EDT 2021. Contains 342920 sequences. (Running on oeis4.)