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

Author

T. D. Noe, May 13 2005

Keywords

• nonn
• easy

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)

Crossrefs

Cf. A139827.

Programs

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

Mathematica

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

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

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