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

2,1

Links

Table of n, a(n) for n=2..78.

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

Example

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.

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

Prog

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

Crossrefs

Cf. A045917, A187129, A186201, A362641.

Sequence in context: A295725 A132822 A347823 * A329803 A355196 A202818

Adjacent sequences: A185294 A185295 A185296 * A185298 A185299 A185300

Keyword

nonn

Author

N. J. A. Sloane, Mar 11 2011

Status

approved