A172989 Smallest k such that the two numbers n^2 +- k are primes.

1, 2, 3, 6, 5, 12, 3, 2, 3, 18, 5, 12, 3, 2, 15, 18, 7, 12, 21, 2, 63, 42, 55, 6, 15, 10, 27, 12, 19, 78, 15, 2, 93, 12, 5, 78, 15, 10, 21, 12, 23, 18, 57, 14, 27, 30, 7, 120, 117, 8, 15, 42, 37, 24, 27, 58, 93, 18, 7, 12, 75, 38, 3, 6, 7, 132, 27, 28, 69, 18, 5, 102, 27, 34, 75, 78, 5

Offset: 2

Author

Vladimir Joseph Stephan Orlovsky, Feb 07 2010

Keywords

• nonn

Examples

			2^2 +- 1 are both prime, 3^2 +- 2 are both prime, 4^2 +- 3 are both prime, 5^2 +- 6 are both prime, ...
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A060272 (at least one prime), A082467 (supersequence).

Programs

Magma

sol:=[]; for m in [2..80] do for k in [1..200] do if IsPrime(m^2-k) and IsPrime(m^2+k) then sol[m-1]:=k; break; end if; end for; end for; sol; // Marius A. Burtea, Jul 28 2019

Mathematica

f[n_]:=Block[{k},If[OddQ[n],k=2,k=1];While[ !PrimeQ[n-k]||!PrimeQ[n+k],k+=2];k];Table[f[n^2],{n,2,40}]

PARI

a(n) = my(k=1); while(!isprime(n^2+k) || !isprime(n^2-k), k++); k; \\ Michel Marcus, May 20 2018

Formula

a(n) = A082467(n^2). - Ivan N. Ianakiev, Jul 28 2019