A338770 a(n) is the sum of primes of the form n - 2*p for primes p < n/2.

0, 0, 0, 0, 0, 2, 3, 2, 8, 0, 12, 2, 10, 0, 16, 2, 34, 0, 18, 0, 35, 0, 49, 2, 33, 0, 58, 2, 52, 0, 22, 0, 89, 0, 73, 2, 68, 0, 64, 2, 97, 0, 88, 0, 132, 0, 134, 2, 80, 0, 189, 0, 147, 0, 87, 0, 227, 0, 103, 2, 73, 0, 241, 2, 223, 0, 189, 0, 221, 0, 178, 0, 184, 0, 322, 2, 307, 0, 189, 0, 336, 0

Offset

1,6

Comments

If n is even then a(n)=2*A010051(n/2-1).

Links

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

Example

The representations of 31 as 2*p+q with p and q prime are 2*7+17 and 2*13+5, so a(31) = 17 + 5 = 22.

Maple

f:= proc(n) local q, v, t;
  t:= 0; q:= 1;
  do
    q:= nextprime(q);
    if 2*q > n then return t fi;
    v:= n - 2*q;
    if isprime(v) then t:= t+v fi;
  od;
end proc:
map(f, [$1..100]);

Prog

(PARI) a(n) = my(s=0); forprime(p=0, n\2, if (isprime(q=n-2*p), s+=q)); s; \\ Michel Marcus, Nov 08 2020

Crossrefs

Cf. A010051.

Sequence in context: A048601 A008317 A139011 * A063708 A096488 A011280

Adjacent sequences: A338767 A338768 A338769 * A338771 A338772 A338773

Keyword

nonn,look

Author

J. M. Bergot and Robert Israel, Nov 08 2020

Status

approved