A343564 a(n) is the sum of 2*n mod p for primes p such that 2*n-p is prime.

0, 0, 0, 5, 4, 7, 5, 10, 19, 18, 11, 32, 17, 25, 45, 24, 25, 56, 10, 45, 66, 32, 39, 96, 68, 55, 99, 59, 46, 148, 29, 104, 138, 49, 103, 162, 81, 112, 164, 91, 109, 260, 64, 105, 316, 115, 104, 235, 119, 202, 294, 188, 127, 319, 224, 251, 409, 177, 162, 500, 124, 181, 504, 135, 315, 437, 187, 271

Offset: 1

Author

J. M. Bergot and Robert Israel, Apr 20 2021

Keywords

• nonn

Comments

Conjecture: the only n for which a(n) <= n are 1, 2, 3, 5, 7, 11, 19, and 31.

Examples

			For n=5, we have 2*n = 3+7 = 5+5, and a(5) = (10 mod 3)+(10 mod 5)+(10 mod 7) = 1+0+3 = 4.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A171637, A343566.

Programs

Maple

N:= 1000: # for a(1)..a(N)
P:= select(isprime,[seq(i,i=3..2*N)]):
f:= proc(n) local m,Q,q;
  m:= ListTools:-BinaryPlace(P,2*n);
  Q:= convert(P[1..m],set);
  Q:= Q intersect map(t -> 2*n-t, Q);
  add(2*n mod q, q = Q);
end proc:
map(f, [$1..N]);

PARI

a(n) = my(p=2, s=0); forprime(p=2, 2*n, if (isprime(2*n-p), s += (2*n % p))); s; \\ Michel Marcus, Apr 20 2021