A139982 Primes of the form 20x^2+20xy+43y^2.

43, 83, 163, 283, 347, 443, 467, 587, 643, 883, 947, 1163, 1187, 1483, 1787, 1867, 1907, 1987, 2243, 2267, 2467, 2683, 2707, 3083, 3163, 3203, 3307, 3323, 3467, 3923, 4243, 4507, 4523, 4547, 4603, 4643, 4723, 4987, 5003, 5147, 5443, 5483

Offset

1,1

Comments

Discriminant=-3040. 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, 83, 123, 163, 187, 267, 283, 347, 387, 403, 427, 443, 467, 587, 643, 707, 723, 747, 803, 843, 883, 923, 947, 1027, 1043, 1107, 1147, 1163, 1187, 1203, 1227, 1347, 1403, 1467, 1483, 1507, 1563, 1603, 1643, 1683, 1707, 1787, 1803, 1867, 1907, 1923, 1947, 1963, 1987, 2107, 2163, 2227, 2243, 2267, 2323, 2363, 2403, 2443, 2467, 2547, 2563, 2627, 2667, 2683, 2707, 2723, 2747, 2867, 2923, 2987, 3003, 3027} (mod 3040).

Mathematica

QuadPrimes2[20, -20, 43, 10000] (* see A106856 *)

Prog

(Magma) [p: p in PrimesUpTo(6000) | p mod 3040 in [43, 83, 123, 163, 187, 267, 283, 347, 387, 403, 427, 443, 467, 587, 643, 707, 723, 747, 803, 843, 883, 923, 947, 1027, 1043, 1107, 1147, 1163, 1187, 1203, 1227, 1347, 1403, 1467, 1483, 1507, 1563, 1603, 1643, 1683, 1707, 1787, 1803, 1867, 1907, 1923, 1947, 1963, 1987, 2107, 2163, 2227, 2243, 2267, 2323, 2363, 2403, 2443, 2467, 2547, 2563, 2627, 2667, 2683, 2707, 2723, 2747, 2867, 2923, 2987, 3003, 3027]]; // Vincenzo Librandi, Aug 03 2012

Crossrefs

Sequence in context: A183074 A289730 A045238 * A171252 A119487 A180549

Adjacent sequences: A139979 A139980 A139981 * A139983 A139984 A139985

Keyword

nonn,easy

Author

T. D. Noe, May 02 2008

Status

approved