A279481 Count the primes appearing in each interval [p,q] where (p,q) is a Goldbach partition of 2n, and then add the results.

0, 0, 1, 2, 4, 2, 5, 8, 6, 9, 13, 12, 14, 10, 12, 12, 24, 22, 9, 20, 24, 27, 29, 38, 36, 24, 39, 29, 33, 43, 24, 58, 58, 17, 52, 60, 53, 63, 80, 46, 54, 87, 70, 46, 100, 62, 58, 87, 31, 79, 104, 71, 87, 119, 99, 116, 152, 114, 94, 181, 54, 82, 144, 39, 116, 133

Offset

1,4

Links

Table of n, a(n) for n=1..66.

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=2..n} A010051(i)*A010051(2*n-i)*(pi(2*n-i)-pi(i-1)) for n > 2.

Maple

with(numtheory): A279481:=n->add( (pi(i)-pi(i-1)) * (pi(2*n-i)-pi(2*n-i-1)) * (pi(2*n-i)-pi(i-1)), i=2..n): 0, 0, seq(A279481(n), n=3..100);

Mathematica

f[n_] := Sum[ Boole[ PrimeQ[ i]] Boole[ PrimeQ[ 2n -i]] (PrimePi[ 2n -i] - PrimePi[i -1]), {i, 2, n}]; f[2] = 0; Array[ f, 80] (* Robert G. Wilson v, Dec 15 2016 *)

Crossrefs

Cf. A000720, A010051, A045917, A278700, A279103.

Sequence in context: A267005 A347796 A011169 * A233131 A202395 A117903

Adjacent sequences: A279478 A279479 A279480 * A279482 A279483 A279484

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Dec 12 2016

Status

approved