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

%I

%S 7,79,127,151,271,439,607,919,967,1063,1231,1327,1399,1447,1471,1663,

%T 1759,1999,2239,2287,2383,2503,2551,2647,2719,2767,2791,3079,3319,

%U 3343,3511,3559,3583,3607,3823,3847,3967,4111,4231,4567,4639,4663

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

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

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

%o (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 Cf. A140633.

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 19 2008

%E Incorrect Mathematica program deleted by _N. J. A. Sloane_, Jun 07 2014

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Last modified May 14 22:40 EDT 2021. Contains 343909 sequences. (Running on oeis4.)