A185297 Consider all pairs of primes (p,q) with p+q = 2n, p <= q; a(n) is the sum of all the p's.

2, 3, 3, 8, 5, 10, 8, 12, 10, 19, 23, 23, 16, 31, 16, 36, 42, 26, 31, 48, 23, 48, 59, 42, 39, 71, 35, 62, 108, 53, 59, 96, 38, 83, 108, 91, 77, 127, 76, 107, 178, 85, 92, 217, 66, 127, 169, 87, 148, 204, 121, 148, 196, 134, 165, 268, 122, 168, 358, 136, 145, 340, 111, 219, 323, 206, 157, 282, 255, 272, 373, 246, 175, 486, 132, 260, 419

Offset: 2

Author

N. J. A. Sloane, Mar 11 2011

Keywords

• nonn

Examples

			2*5 = 10 can be expressed as the sum of two primes in two ways, 3+7 and 5+5, so a(5) = 3+5 = 8.
		

Crossrefs

Cf. A045917, A187129, A186201, A362641.

Programs

Maple

with(numtheory);
a:=n-> sum( (i)*( ((pi(i) - pi(i-1)) * (pi(2*n-i) - pi(2*n-i-1))) ), i = 1..n ); seq(a(k),k=1..100); # Wesley Ivan Hurt, Jan 20 2013

PARI

a(n) = my(s=0); forprime(p=1, n, if (isprime(2*n-p), s += p)); s; \\ Michel Marcus, Apr 29 2021

Formula

a(n) = Sum_{i=1..n} i * c(i) * c(2*n-i), where c = A010051. - Wesley Ivan Hurt, Apr 29 2021

a(n) = sopf(A362641(n)), n>=2. - Wesley Ivan Hurt, Apr 28 2023