A293271 Numbers n such that n - p and n + p are both prime for some prime p.

5, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 30, 32, 34, 36, 39, 40, 42, 44, 45, 46, 48, 50, 54, 56, 60, 64, 66, 69, 70, 72, 76, 78, 81, 84, 86, 90, 92, 96, 99, 100, 102, 104, 105, 106, 108, 110, 111, 114, 116, 120, 126, 129, 130, 132, 134, 138, 140, 142

Offset: 1

Author

Gionata Neri, Oct 04 2017

Keywords

• nonn

Comments

Apart from a(1), all terms are composite.

Union of A087679 and 2*A063713. - Robert Israel, Oct 09 2017

Crossrefs

Cf. A087679, A087695, A087696, A087697 (subsequences).

Cf. A063713.

Programs

Maple

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

Mathematica

Select[Range@ 142, Function[n, AnyTrue[Prime@ Range@ PrimePi@ n, PrimeQ[n + {-#, #}] == {True, True} &]]] (* Michael De Vlieger, Oct 09 2017 *)

PARI

a(n) = forprime(p=1, n, i=n-p; j=n+p; if(isprime(i)&&isprime(j), n; break))