A139896 Primes of the form 8x^2+8xy+31y^2.

31, 47, 79, 127, 191, 263, 271, 311, 359, 367, 479, 503, 599, 607, 727, 743, 751, 823, 839, 887, 911, 967, 983, 1063, 1087, 1279, 1303, 1319, 1423, 1439, 1447, 1471, 1487, 1511, 1583, 1607, 1663, 1759, 1783, 1871, 1951, 1999, 2143, 2207, 2351

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-928. 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 232 in [15, 31, 39, 47, 55, 79, 95, 119, 127, 135, 143, 159, 191, 215]]; // Vincenzo Librandi, Jul 31 2012

Mathematica

QuadPrimes2[8, -8, 31, 10000] (* see A106856 *)

Formula

The primes are congruent to {15, 31, 39, 47, 55, 79, 95, 119, 127, 135, 143, 159, 191, 215} (mod 232).