A063713 -id:A063713 - cp's OEIS frontend

A063714 Values of r occurring in A063713.

3, 3, 5, 3, 3, 5, 3, 19, 5, 3, 7, 29, 3, 5, 3, 5, 3, 43, 5, 3, 7, 3, 7, 3, 5, 3, 11, 3, 5, 5, 3, 7, 89, 7, 3, 5, 3, 3, 5, 3, 13, 113, 7, 13, 127, 5, 3, 11, 137, 139, 5, 13, 3, 7, 3, 5, 5, 3, 7, 3, 13, 5, 19, 3, 3, 31, 197, 199, 7, 13, 17, 11, 3, 5, 3, 229, 5, 3, 11, 5, 11, 3, 19, 3, 7, 3, 7

Offset: 1

Reinhard Zumkeller, Aug 10 2001

This is not a mere union of A002373 and A020483 because of the minimality property of these sequences.

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

Cf. A063713, A002373, A020483.

f:= proc(n) local k;
k:= 2;
  while k < 2*n do
   k:= nextprime(k);
    if isprime(2*n+k) and isprime(2*n-k) then return k fi
  od;
  NULL
end proc:
map(f, [$1..400]); # Robert Israel, Oct 09 2017

f[n_] := {AnyTrue[Prime[Range[PrimePi[2n-2]]], (r = #; PrimeQ[2n+r] && PrimeQ[2n-r])&], r}; Select[f /@ Range[200], #[[1]] =!= False &][[All, 2]] (* Jean-François Alcover, Feb 14 2018 *)

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

Original entry on oeis.org

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

Gionata Neri, Oct 04 2017

nonn

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

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

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

Cf. A063713.

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

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

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

cp's OEIS Frontend

A063714 Values of r occurring in A063713.

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