A139906 Primes of the form 17x^2+12xy+17y^2.

17, 61, 109, 149, 241, 281, 293, 337, 373, 457, 557, 569, 613, 677, 701, 733, 769, 937, 941, 953, 1009, 1033, 1069, 1201, 1217, 1229, 1249, 1493, 1597, 1601, 1693, 1801, 1861, 1877, 1949, 1993, 1997, 2081, 2089, 2153, 2213, 2273, 2389, 2437

Offset

1,1

Comments

Discriminant=-1012. 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 {17, 21, 57, 61, 65, 109, 129, 145, 149, 153, 189, 205, 217, 237, 241, 249, 281, 293, 321, 329, 337, 365, 373, 413, 425, 457, 481, 497, 505, 513, 525, 549, 557, 569, 585, 589, 613, 677, 681, 689, 701, 733, 769, 789, 833, 849, 865, 893, 937, 941, 953, 965, 981, 985, 1009} (mod 1012).

Mathematica

Union[QuadPrimes2[17, 12, 17, 10000], QuadPrimes2[17, -12, 17, 10000]] (* see A106856 *)

Prog

(Magma) [ p: p in PrimesUpTo(3000) | p mod 1012 in {17, 21, 57, 61, 65, 109, 129, 145, 149, 153, 189, 205, 217, 237, 241, 249, 281, 293, 321, 329, 337, 365, 373, 413, 425, 457, 481, 497, 505, 513, 525, 549, 557, 569, 585, 589, 613, 677, 681, 689, 701, 733, 769, 789, 833, 849, 865, 893, 937, 941, 953, 965, 981, 985, 1009}]; // Vincenzo Librandi, Jul 31 2012

Crossrefs

Sequence in context: A094207 A156912 A141853 * A117874 A039607 A142299

Adjacent sequences: A139903 A139904 A139905 * A139907 A139908 A139909

Keyword

nonn,easy

Author

T. D. Noe, May 02 2008

Status

approved