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A279728 Sum of the larger parts of the Goldbach partitions (p,q) of 2n such that all primes from p to q (inclusive) appear as a part in some Goldbach partition of p+q = 2n. 5
0, 0, 3, 5, 12, 7, 7, 0, 24, 0, 11, 49, 13, 0, 59, 0, 17, 42, 19, 0, 23, 0, 23, 0, 0, 29, 0, 0, 29, 199, 31, 0, 0, 37, 0, 0, 37, 0, 41, 0, 41, 143, 43, 0, 47, 0, 47, 0, 0, 53, 0, 0, 112, 0, 0, 59, 0, 0, 59, 128, 61, 0, 0, 67, 0, 0, 67, 0, 71, 0, 71, 73, 73, 0, 0, 79, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..78.

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

MAPLE

with(numtheory): A279728:=n->add( (2*n-i) * (pi(i)-pi(i-1)) * (pi(2*n-i)-pi(2*n-i-1)) * (product(1-abs((pi(k)-pi(k-1))-(pi(2*n-k)-pi(2*n-k-1))), k=i..n)), i=3..n): seq(A279728(n), n=1..100);

MATHEMATICA

Table[Sum[((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}], {n, 100}] (* Michael De Vlieger, Dec 18 2016 *)

CROSSREFS

Cf. A010051, A279315, A279727, A279729.

Sequence in context: A101315 A320433 A066541 * A087122 A286900 A037221

Adjacent sequences:  A279725 A279726 A279727 * A279729 A279730 A279731

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Dec 17 2016

STATUS

approved

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Last modified February 25 05:15 EST 2020. Contains 332217 sequences. (Running on oeis4.)