A045373 - OEIS

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

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OFFSET

1,1

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)

MATHEMATICA

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

PROG

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

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

CROSSREFS

Primes in A028951.

Cf. A191017, A003625 (complement).

Sequence in context: A160698 A294114 A144707 * A075431 A184799 A045374

Adjacent sequences: A045370 A045371 A045372 * A045374 A045375 A045376

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved