A238778 Sum of all primes p such that 2n - p is also a prime.

2, 3, 8, 15, 12, 21, 32, 36, 40, 55, 72, 65, 56, 90, 64, 119, 144, 57, 120, 168, 132, 161, 240, 200, 156, 270, 168, 203, 360, 155, 320, 396, 136, 350, 432, 333, 380, 546, 320, 369, 672, 387, 352, 810, 368, 423, 672, 294, 600, 816, 520, 583, 864, 660, 784

Offset: 2

Author

Reinhard Zumkeller, Mar 06 2014

Keywords

• nonn

Comments

Sum of n-th row in triangle A171637.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A008472, A238711.

Cf. A010051, A035026, A171637

Programs

Haskell

a238778 n = sum $ filter ((== 1) . a010051') $
   map (2 * n -) $ takeWhile (<= 2 * n) a000040_list

Mathematica

Table[Total@Select[Select[Prime[Range[2 n]], # < 2 n &], PrimeQ[2 n - #] &], {n, 2, 56}] (* Robert Price, Apr 26 2025 *)

PARI

a(n) = my(s=0); forprime(p=2, 2*n, if(isprime(2*n-p), s+=p)); s; \\ Michel Marcus, Jan 24 2022

Formula

a(n) = A008472(A238711(n)).

a(n) mod 2 = A010051(n).

a(n) = n*A035026(n). - Robert G. Wilson v, Apr 28 2018