A139941 Primes of the form 19x^2+8xy+19y^2.

19, 79, 199, 379, 571, 619, 631, 751, 919, 1171, 1279, 1399, 1459, 1471, 1579, 1699, 1759, 1831, 1951, 1999, 2011, 2131, 2179, 2251, 2311, 2551, 2659, 2719, 2731, 2851, 3079, 3271, 3319, 3331, 3391, 3511, 3559, 3631, 3691, 3931, 4099, 4111

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-1380. 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(6000) | p mod 1380 in [19, 79, 91, 199, 319, 379, 451, 511, 559, 571, 619, 631, 751, 799, 871, 919, 931, 1111, 1171, 1279, 1339, 1351]]; // Vincenzo Librandi, Aug 02 2012

Mathematica

Union[QuadPrimes2[19, 8, 19, 10000], QuadPrimes2[19, -8, 19, 10000]] (* see A106856 *)

Formula

The primes are congruent to {19, 79, 91, 199, 319, 379, 451, 511, 559, 571, 619, 631, 751, 799, 871, 919, 931, 1111, 1171, 1279, 1339, 1351} (mod 1380).