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A279481
Count the primes appearing in each interval [p,q] where (p,q) is a Goldbach partition of 2n, and then add the results.
4
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
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Dec 12 2016
STATUS
approved