A139949 Primes of the form 2x^2+2xy+193y^2.

2, 193, 197, 233, 277, 337, 373, 457, 557, 613, 673, 877, 953, 1033, 1117, 1297, 1493, 1597, 1733, 1877, 1913, 1933, 1997, 2053, 2153, 2213, 2417, 2437, 2657, 2713, 2837, 2857, 3137, 3313, 3593, 3637, 4153, 4253, 4397, 4517, 4813, 4817

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-1540. 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)

Programs

Magma

[ p: p in PrimesUpTo(6000) | p mod 1540 in [2, 57, 193, 197, 233, 277, 337, 373, 393, 417, 457, 513, 557, 613, 673, 813, 877, 893, 897, 953, 1033, 1073, 1117, 1157, 1173, 1297, 1317, 1437, 1493, 1513, 1537]]; // Vincenzo Librandi, Aug 03 2012

Mathematica

QuadPrimes2[2, -2, 193, 10000] (* see A106856 *)

Formula

The primes are congruent to {2, 57, 193, 197, 233, 277, 337, 373, 393, 417, 457, 513, 557, 613, 673, 813, 877, 893, 897, 953, 1033, 1073, 1117, 1157, 1173, 1297, 1317, 1437, 1493, 1513, 1537} (mod 1540).