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

1,1

Links

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

Example

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.

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 *)

Crossrefs

Cf. A063714, A002373, A020483.

Sequence in context: A026425 A026440 A299487 * A026462 A039230 A111222

Adjacent sequences: A063710 A063711 A063712 * A063714 A063715 A063716

Keyword

nonn

Author

Reinhard Zumkeller, Aug 10 2001

Status

approved