A107188 Primes of the form 6x^2 + 13y^2.

13, 19, 37, 67, 109, 163, 229, 307, 331, 349, 379, 397, 421, 499, 541, 613, 619, 643, 661, 691, 709, 733, 739, 787, 811, 853, 877, 1021, 1051, 1123, 1237, 1549, 1579, 1597, 1627, 1669, 1723, 1747, 1789, 1861, 1867, 1987, 2179, 2203, 2221, 2251

Offset

1,1

Comments

Discriminant = -312. 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 {13, 19, 37, 67, 85, 109, 115, 163, 187, 229, 253, 301, 307} (mod 312). - T. D. Noe, May 02 2008

Mathematica

QuadPrimes2[6, 0, 13, 10000] (* see A106856 *)

Prog

(Magma) [ p: p in PrimesUpTo(3000) | p mod 312 in {13, 19, 37, 67, 85, 109, 115, 163, 187, 229, 253, 301, 307} ]; // Vincenzo Librandi, Jul 26 2012
(PARI) list(lim)=my(v=List([13]), s=[19, 37, 67, 85, 109, 115, 163, 187, 229, 253, 301, 307]); forprime(p=19, lim, if(setsearch(s, p%312), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

Crossrefs

Cf. A139827.

Sequence in context: A048523 A307627 A000922 * A029478 A252021 A216101

Adjacent sequences: A107185 A107186 A107187 * A107189 A107190 A107191

Keyword

nonn,easy

Author

T. D. Noe, May 13 2005

Status

approved