A139866 Primes of the form 13x^2 + 12xy + 13y^2.

13, 41, 89, 97, 173, 181, 241, 257, 269, 293, 409, 433, 509, 521, 601, 661, 677, 773, 797, 829, 857, 941, 1021, 1097, 1153, 1181, 1193, 1237, 1249, 1321, 1361, 1433, 1553, 1609, 1637, 1693, 1741, 1777, 1861, 1889, 2029, 2089, 2141, 2161, 2273

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant = -532. See A139827 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)

Programs

Magma

[ p: p in PrimesUpTo(3000) | p mod 532 in {13, 33, 41, 69, 89, 97, 117, 129, 145, 173, 181, 185, 241, 257, 265, 269, 293, 297, 325, 341, 369, 409, 433, 489, 493, 509, 521}]; // Vincenzo Librandi, Jul 29 2012

Mathematica

Union[QuadPrimes2[13, 12, 13, 10000], QuadPrimes2[13, -12, 13, 10000]] (* see A106856 *)

Formula

The primes are congruent to {13, 33, 41, 69, 89, 97, 117, 129, 145, 173, 181, 185, 241, 257, 265, 269, 293, 297, 325, 341, 369, 409, 433, 489, 493, 509, 521} (mod 532).