A140018 Primes of the form 7x^2+195y^2.

7, 223, 307, 643, 787, 1123, 1567, 1627, 1783, 1867, 1987, 2203, 2803, 3307, 3463, 3547, 3583, 3967, 4483, 4903, 4987, 5323, 5647, 5683, 6247, 6823, 7027, 7243, 7507, 7867, 8263, 8287, 8923, 9007, 9043, 9547, 10303, 10723, 11863, 12043

Offset

1,1

Comments

Discriminant=-5460. 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)

Formula

The primes are congruent to {7, 187, 223, 307, 643, 787, 943, 1123, 1207, 1363, 1567, 1627, 1783, 1867, 1903, 1987, 2047, 2203, 2407, 2803, 2827, 3127, 3307, 3463, 3547, 3583, 3967, 4063, 4087, 4387, 4483, 4843, 4903, 4987, 5143, 5263, 5323} (mod 5460).

Mathematica

QuadPrimes2[7, 0, 195, 10000] (* see A106856 *)
With[{nn=50}, Take[Select[Union[7First[#]^2+195Last[#]^2&/@Tuples[ Range[ 0, nn], 2]], PrimeQ], nn]] (* Harvey P. Dale, Aug 29 2014 *)

Prog

(Magma) [ p: p in PrimesUpTo(13000) | p mod 5460 in {7, 187, 223, 307, 643, 787, 943, 1123, 1207, 1363, 1567, 1627, 1783, 1867, 1903, 1987, 2047, 2203, 2407, 2803, 2827, 3127, 3307, 3463, 3547, 3583, 3967, 4063, 4087, 4387, 4483, 4843, 4903, 4987, 5143, 5263, 5323} ]; // Vincenzo Librandi, Aug 05 2012

Crossrefs

Sequence in context: A145107 A231488 A231487 * A202655 A009488 A302059

Adjacent sequences: A140015 A140016 A140017 * A140019 A140020 A140021

Keyword

nonn,easy

Author

T. D. Noe, May 02 2008

Status

approved