A063713 Numbers n such that there exist primes p, q, r with n*2 = p - r = r + q (values of r are given in A063714).

4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 27, 28, 30, 32, 33, 35, 36, 38, 39, 42, 43, 45, 46, 48, 50, 51, 52, 53, 54, 55, 57, 58, 60, 63, 65, 66, 67, 69, 70, 71, 72, 75, 77, 78, 80, 81, 84, 85, 87, 88, 90, 93, 96, 97, 98, 99, 100, 101, 102, 105

Offset: 1

Author

Reinhard Zumkeller, Aug 10 2001

Keywords

• nonn

Examples

			10*2 = 20 = 23 - 3 = 3 + 17, A063714(7) = 3; 11*2 = 22 = 41 - 19 = 19 + 3, A063714(8) = 19 28 is missing because we have the prime sums (Goldbach): 5 + 23 = 11 + 17 and differences with primes less 28: 31 - 3 = 41 - 13 = 47 - 19; none of these have a prime in common.
		

Links

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

Crossrefs

Cf. A063714, A002373, A020483.

Programs

Maple

filter:= proc(n) local k;
  k:= 1;
  while k < 2*n do
    k:= nextprime(k);
    if isprime(2*n+k) and isprime(2*n-k) then return true fi
  od;
  false
end proc:
select(filter, [$1..1000]); # Robert Israel, Oct 09 2017

Mathematica

okQ[n_] := AnyTrue[Prime[Range[PrimePi[2 n - 2]]], PrimeQ[2 n + #] && PrimeQ[2 n - #]&]; Select[Range[105], okQ] (* Jean-François Alcover, Feb 12 2018 *)