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

Author

Wesley Ivan Hurt, Dec 12 2016

Keywords

• nonn
• easy

Links

• 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

Crossrefs

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

Programs

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 *)

Formula

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