cp's OEIS Frontend

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

%I A140613 #36 Feb 09 2018 03:11:08
%S A140613 7,79,127,151,271,439,607,919,967,1063,1231,1327,1399,1447,1471,1663,
%T A140613 1759,1999,2239,2287,2383,2503,2551,2647,2719,2767,2791,3079,3319,
%U A140613 3343,3511,3559,3583,3607,3823,3847,3967,4111,4231,4567,4639,4663
%N A140613 Primes of the form 7*x^2 + 6*x*y + 39*y^2.
%C A140613 Discriminant=-1056. Also primes of the form 7x^2 + 4xy + 76y^2.
%C A140613 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
%H A140613 Vincenzo Librandi, N. J. A. Sloane and Ray Chandler, <a href="/A140613/b140613.txt">Table of n, a(n) for n = 1..10000</a> [First 1000 terms from Vincenzo Librandi, next 5218 terms from N. J. A. Sloane]
%H A140613 N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)
%H A140613 J. Voight, <a href="https://doi.org/10.1090/S0025-5718-07-01976-X">Quadratic forms that represent almost the same primes</a>, Math. Comp., Vol. 76 (2007), pp. 1589-1617. See Example 6.1. - _N. J. A. Sloane_, Jun 07 2014
%F A140613 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
%t A140613 Union[QuadPrimes2[7, 6, 39, 10000], QuadPrimes2[7, -6, 39, 10000]] (* see A106856 *)
%o A140613 (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
%Y A140613 Cf. A140633.
%K A140613 nonn,easy
%O A140613 1,1
%A A140613 _T. D. Noe_, May 19 2008
%E A140613 Incorrect Mathematica program deleted by _N. J. A. Sloane_, Jun 07 2014