A107165 Primes of the form 3x^2 + 19y^2.

3, 19, 31, 67, 79, 103, 127, 151, 211, 223, 307, 331, 379, 439, 487, 523, 547, 607, 751, 787, 811, 907, 991, 1039, 1063, 1123, 1171, 1231, 1291, 1399, 1447, 1459, 1471, 1579, 1627, 1663, 1699, 1723, 1747, 1951, 2083, 2131, 2143, 2179, 2203

Offset

1,1

Comments

Discriminant = -228. See A107132 for more information.

Links

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Formula

The primes are congruent to {3, 19, 31, 67, 79, 91, 103, 127, 151, 211, 223} (mod 228). - T. D. Noe, May 02 2008

Mathematica

QuadPrimes2[3, 0, 19, 10000] (* see A106856 *)

Prog

(Magma) [p: p in PrimesUpTo(3000) | p mod 228 in [3, 19, 31, 67, 79, 91, 103, 127, 151, 211, 223]]; // Vincenzo Librandi, Jul 25 2012
(PARI) list(lim)=my(v=List([3]), s=[19, 31, 67, 79, 91, 103, 127, 151, 211, 223]); forprime(p=19, lim, if(setsearch(s, p%228), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

Crossrefs

Cf. A139827.

Sequence in context: A218537 A236969 A222590 * A066811 A269414 A162307

Adjacent sequences: A107162 A107163 A107164 * A107166 A107167 A107168

Keyword

nonn,easy

Author

T. D. Noe, May 13 2005

Status

approved