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

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..62.

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 *)

Prog

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

Crossrefs

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

Cf. A063713.

Sequence in context: A293795 A165991 A300331 * A348046 A371656 A323215

Adjacent sequences: A293268 A293269 A293270 * A293272 A293273 A293274

Keyword

nonn

Author

Gionata Neri, Oct 04 2017

Status

approved