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

1,1

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

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A140633.

Sequence in context: A106107 A020471 A065902 * A139945 A023285 A135051

Adjacent sequences: A140610 A140611 A140612 * A140614 A140615 A140616

Keyword

nonn,easy

Author

T. D. Noe, May 19 2008

Extensions

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

Status

approved