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

2,2

Links

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

Formula

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

Example

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

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}]

Prog

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

Crossrefs

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

Sequence in context: A106379 A232929 A001634 * A095113 A345179 A367584

Adjacent sequences: A172986 A172987 A172988 * A172990 A172991 A172992

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Feb 07 2010

Status

approved