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

1,1

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

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 *)

Prog

(PARI) select(n->n%6<5, primes(100)) \\ Charles R Greathouse IV, May 20 2011
(Magma) [p: p in PrimesUpTo(700) | p mod 6 in [1, 2, 3]]; // Vincenzo Librandi, Aug 08 2012
(Haskell)
a045331 n = a045331_list !! (n-1)
a045331_list = filter ((< 4) . (`mod` 6)) a000040_list
-- Reinhard Zumkeller, Jan 15 2013

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.

Sequence in context: A051484 A101415 A210393 * A053613 A013645 A130272

Adjacent sequences: A045328 A045329 A045330 * A045332 A045333 A045334

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

More terms from Henry Bottomley, Aug 10 2000

Status

approved