A140020 Primes of the form 13x^2+105y^2.

13, 157, 313, 433, 937, 997, 1153, 1693, 1777, 1993, 2617, 2677, 2833, 3253, 3433, 3457, 3793, 3877, 4177, 4273, 5113, 5197, 5437, 5953, 6373, 6397, 6733, 7237, 7297, 7537, 8293, 8713, 8893, 9337, 9733, 10477, 10513, 10657, 11353, 11437

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 1556 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 {13, 157, 313, 433, 493, 517, 913, 937, 997, 1153, 1273, 1693, 1777, 1837, 1993, 2077, 2497, 2617, 2677, 2833, 3013, 3097, 3253, 3337, 3433, 3457, 3793, 3877, 4177, 4213, 4273, 5017, 5053, 5113, 5197, 5353, 5437} (mod 5460).

Mathematica

QuadPrimes2[13, 0, 105, 10000] (* see A106856 *)

Prog

(Magma) [ p: p in PrimesUpTo(13000) | p mod 5460 in {13, 157, 313, 433, 493, 517, 913, 937, 997, 1153, 1273, 1693, 1777, 1837, 1993, 2077, 2497, 2617, 2677, 2833, 3013, 3097, 3253, 3337, 3433, 3457, 3793, 3877, 4177, 4213, 4273, 5017, 5053, 5113, 5197, 5353, 5437} ]; // Vincenzo Librandi, Aug 05 2012

Crossrefs

Sequence in context: A360172 A250210 A142104 * A130868 A154414 A164623

Adjacent sequences: A140017 A140018 A140019 * A140021 A140022 A140023

Keyword

nonn,easy

Author

T. D. Noe, May 02 2008

Status

approved