A187129 Consider all pairs of primes (p,q) with p+q = 2n, p <= q; a(n) is the sum of all the q's.

2, 3, 5, 12, 7, 18, 24, 24, 30, 47, 49, 55, 40, 59, 48, 100, 102, 50, 89, 120, 109, 136, 181, 158, 117, 199, 133, 170, 252, 133, 261, 300, 98, 267, 324, 279, 303, 419, 244, 303, 494, 345, 260, 593, 302, 343, 503, 207, 452, 612, 399, 488, 668, 526, 619, 872, 574, 540, 1082, 352, 475, 920, 273, 691, 865, 598, 523, 822, 725, 864, 1211

Offset

2,1

Links

Harvey P. Dale, Table of n, a(n) for n = 2..1000

Formula

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

a(n) = sopf(A362640(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) = 7+5 = 12.

Maple

with(numtheory); a:=n-> sum( (2*n-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

Mathematica

Table[Total[Select[IntegerPartitions[2*n, {2}], AllTrue[#, PrimeQ]&][[All, 1]]], {n, 2, 100}] (* Harvey P. Dale, Aug 09 2020 *)

Prog

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

Crossrefs

Cf. A045917, A185297, A186201, A362640.

Sequence in context: A321855 A357433 A112978 * A341700 A158936 A271227

Adjacent sequences: A187126 A187127 A187128 * A187130 A187131 A187132

Keyword

nonn

Author

N. J. A. Sloane, Mar 11 2011

Status

approved