A056896 Smallest prime which can be written as k^2 + n for k >= 0.

2, 2, 3, 5, 5, 7, 7, 17, 13, 11, 11, 13, 13, 23, 19, 17, 17, 19, 19, 29, 37, 23, 23, 73, 29, 107, 31, 29, 29, 31, 31, 41, 37, 43, 71, 37, 37, 47, 43, 41, 41, 43, 43, 53, 61, 47, 47, 73, 53, 59, 67, 53, 53, 79, 59, 137, 61, 59, 59, 61, 61, 71, 67, 73, 101, 67, 67, 149, 73, 71

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = A056897(n)+n = A056898(n)^2+n.

For p a prime: a(p)=p (and a(p-1)=p if p<>3).

Example

a(8)=17 because 17=3^2+8.

Mathematica

Table[k = 0; While[p = n + k^2; ! PrimeQ[p], k++]; p, {n, 100}] (* T. D. Noe, Apr 01 2011 *)
spk[n_]:=Module[{k=0}, While[!PrimeQ[k^2+n], k++]; k^2+n]; Array[spk, 70] (* Harvey P. Dale, Nov 02 2025 *)

Crossrefs

Cf. A000040, A002496, A056892-A056898.

Sequence in context: A151800 A259430 A290838 * A089366 A113827 A033189

Adjacent sequences: A056893 A056894 A056895 * A056897 A056898 A056899

Keyword

nonn

Author

Henry Bottomley, Jul 05 2000

Extensions

Example corrected by Harvey P. Dale, Apr 01 2011

Status

approved