A065376 Primes of the form p + k^2, p prime and k > 0.

3, 7, 11, 17, 19, 23, 29, 41, 43, 47, 53, 59, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307

Offset

1,1

Comments

Conjectured to contain all primes > 7549. - Robert Israel, Sep 03 2014

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Example

a(3) = 11 = 2 + 3^2 = 7 + 2^2.

Maple

N = 1000: # to get all entries <= N
Primes:= select(isprime, {$1..N}):
Primes intersect {seq(seq(p + k^2, p = Primes), k=1..floor(sqrt(N)))}; # Robert Israel, Sep 03 2014

Mathematica

q[n_] := AnyTrue[Range[Floor[Sqrt[n]]], PrimeQ[n - #^2] &]; seq[lim_] := Module[{p = Prime[Range[lim]]}, Select[p, q]]; seq[100] (* Amiram Eldar, Apr 12 2025 *)
Take[Select[Union[Flatten[Table[p+k^2, {p, Prime[Range[70]]}, {k, 100}]]], PrimeQ], 80] (* Harvey P. Dale, Apr 15 2026 *)

Prog

(PARI) lista(nn) = {forprime(p=2, nn, forprime(q=2, p-1, if (issquare(p-q), print1(p, ", "); break; ); ); ); } \\ Michel Marcus, Sep 03 2014

Crossrefs

Complement of A065377.

Cf. A000040, A000290.

Sequence in context: A112786 A023211 A038981 * A130090 A136059 A156284

Adjacent sequences: A065373 A065374 A065375 * A065377 A065378 A065379

Keyword

nonn

Author

Reinhard Zumkeller, Nov 03 2001

Status

approved