A140028 Primes of the form 42x^2+42xy+43y^2.

43, 127, 547, 823, 883, 907, 1303, 1327, 1663, 2083, 3067, 3823, 3847, 3943, 4027, 4447, 4603, 4663, 4783, 5443, 5503, 6007, 6343, 6367, 6763, 6967, 7687, 7723, 8467, 8527, 8563, 8863, 9283, 9403, 9643, 9907, 10243, 10663, 10903, 11047

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 {43, 127, 547, 667, 823, 883, 907, 1303, 1327, 1387, 1507, 1663, 1843, 1927, 2083, 2167, 2227, 2263, 3007, 3067, 3103, 3403, 3487, 3823, 3847, 3943, 4027, 4183, 4267, 4447, 4603, 4663, 4783, 5203, 5287, 5443} (mod 5460).

Mathematica

QuadPrimes2[42, -42, 43, 10000] (* see A106856 *)

Prog

(Magma) [ p: p in PrimesUpTo(13000) | p mod 5460 in {43, 127, 547, 667, 823, 883, 907, 1303, 1327, 1387, 1507, 1663, 1843, 1927, 2083, 2167, 2227, 2263, 3007, 3067, 3103, 3403, 3487, 3823, 3847, 3943, 4027, 4183, 4267, 4447, 4603, 4663, 4783, 5203, 5287, 5443} ]; // Vincenzo Librandi, Aug 06 2012

Crossrefs

Sequence in context: A356510 A124826 A136069 * A199818 A248401 A136074

Adjacent sequences: A140025 A140026 A140027 * A140029 A140030 A140031

Keyword

nonn,easy

Author

T. D. Noe, May 02 2008

Status

approved