A045373 Primes congruent to {0, 1, 2, 4} mod 7.

2, 7, 11, 23, 29, 37, 43, 53, 67, 71, 79, 107, 109, 113, 127, 137, 149, 151, 163, 179, 191, 193, 197, 211, 233, 239, 263, 277, 281, 317, 331, 337, 347, 359, 373, 379, 389, 401, 421, 431, 443, 449, 457, 463, 487

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Primes of the form x^2 + xy + 2y^2, discriminant -7. - N. J. A. Sloane, Jun 01 2014

Primes of the form x^2 - xy + 2y^2 with x and y nonnegative. - T. D. Noe, May 07 2005

Also, primes which are squares (mod 7) (or, (mod 14): see A191017 for a sequence formerly defined as such). - M. F. Hasler, Jan 15 2016

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Primes in A028951.

Cf. A191017, A003625 (complement).

Programs

Magma

[p: p in PrimesUpTo(740)|p mod 7 in [0, 1, 2, 4]]; // Vincenzo Librandi, Jul 13 2012

Mathematica

Select[Prime[Range[500]],MemberQ[{0,1,2,4},Mod[#,7]]&] (* Vincenzo Librandi, Jul 13 2012 *)

PARI

select(p->issquare(Mod(p,7))&&isprime(p),[1..1000]) \\ M. F. Hasler, Jan 15 2016