A140613 Primes of the form 7*x^2 + 6*x*y + 39*y^2.

7, 79, 127, 151, 271, 439, 607, 919, 967, 1063, 1231, 1327, 1399, 1447, 1471, 1663, 1759, 1999, 2239, 2287, 2383, 2503, 2551, 2647, 2719, 2767, 2791, 3079, 3319, 3343, 3511, 3559, 3583, 3607, 3823, 3847, 3967, 4111, 4231, 4567, 4639, 4663

Offset: 1

Author

T. D. Noe, May 19 2008

Keywords

• nonn
• easy

Comments

Discriminant=-1056. Also primes of the form 7x^2 + 4xy + 76y^2.

In base 12, the sequence is 7, 67, X7, 107, 1X7, 307, 427, 647, 687, 747, 867, 927, 987, X07, X27, E67, 1027, 11X7, 1367, 13X7, 1467, 1547, 1587, 1647, 16X7, 1727, 1747, 1947, 1E07, 1E27, 2047, 2087, 20X7, 2107, 2267, 2287, 2367, 2467, 2547, 2787, 2827, 2847, where X is 10 and E is 11. Moreover, the discriminant is -740. - Walter Kehowski, Jun 01 2008

Links

• Vincenzo Librandi, N. J. A. Sloane and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi, next 5218 terms from N. J. A. Sloane]
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
• J. Voight, Quadratic forms that represent almost the same primes, Math. Comp., Vol. 76 (2007), pp. 1589-1617. See Example 6.1. - _N. J. A. Sloane_, Jun 07 2014

Crossrefs

Cf. A140633.

Programs

Mathematica

Union[QuadPrimes2[7, 6, 39, 10000], QuadPrimes2[7, -6, 39, 10000]] (* see A106856 *)

PARI

select(n-> n%264==7 || n%264==79 || n%264==127 || n%264==151 || n%264==175, primes(100000)) \\ N. J. A. Sloane, Jun 07 2014

Formula

These are exactly the primes congruent to one of 7, 79, 127, 151, or 175 (mod 264) [Voight]. - N. J. A. Sloane, Jun 07 2014

Extensions

Incorrect Mathematica program deleted by N. J. A. Sloane, Jun 07 2014