A042998 Primes congruent to {1, 2, 3, 5} (mod 8).

2, 3, 5, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 61, 67, 73, 83, 89, 97, 101, 107, 109, 113, 131, 137, 139, 149, 157, 163, 173, 179, 181, 193, 197, 211, 227, 229, 233, 241, 251, 257, 269, 277, 281, 283, 293, 307

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Primes of the form x^2 + y^2 + z^2.

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)
• Wikipedia, Legendre's three-square theorem

Crossrefs

Cf. A000040, A045403.

Programs

Magma

[p: p in PrimesUpTo(500) | p mod 8 in [1, 2, 3, 5]]; // Vincenzo Librandi, Aug 08 2012

Mathematica

Select[Prime[Range[300]],MemberQ[{1,2,3,5},Mod[#,8]]&] (* Vincenzo Librandi, Aug 08 2012 *)

PARI

is(n)=n%8<6 && isprime(n) \\ Charles R Greathouse IV, Sep 15 2015