A045331 Primes congruent to {1, 2, 3} mod 6; or, -3 is a square mod p.

2, 3, 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307, 313, 331, 337, 349, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463, 487, 499, 523, 541, 547, 571, 577, 601, 607, 613

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

Comments

-3 is a quadratic residue mod a prime p iff p is in this sequence.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Apart from initial term, same as A007645; apart from initial two terms, same as A002476.

Cf. A002313, A033203, A038873, A038874, A057128.

Subsequence of A047246.

Programs

Haskell

a045331 n = a045331_list !! (n-1)
a045331_list = filter ((< 4) . (`mod` 6)) a000040_list
-- Reinhard Zumkeller, Jan 15 2013

Magma

[p: p in PrimesUpTo(700) | p mod 6 in [1, 2, 3]]; // Vincenzo Librandi, Aug 08 2012

Mathematica

Select[Prime[Range[200]],MemberQ[{1,2,3},Mod[#,6]]&]  (* Harvey P. Dale, Mar 31 2011 *)
Join[{2,3},Select[Range[7,10^3,6],PrimeQ]] (* Zak Seidov, May 20 2011 *)

PARI

select(n->n%6<5,primes(100)) \\ Charles R Greathouse IV, May 20 2011

Extensions

More terms from Henry Bottomley, Aug 10 2000