A139653 Primes of the form x^2 + 253*y^2.

257, 269, 317, 353, 397, 449, 509, 577, 653, 829, 929, 1013, 1021, 1061, 1093, 1153, 1181, 1237, 1277, 1301, 1373, 1409, 1453, 1549, 1637, 1697, 1741, 1973, 2017, 2237, 2281, 2293, 2341, 2377, 2381, 2473, 2557, 2677, 2693, 2753, 2861, 2953

Offset: 1

Author

T. D. Noe, Apr 29 2008

Keywords

• nonn
• easy

Comments

Discriminant=-1012. See A139643 for more information.

The primes are congruent to {1, 9, 25, 49, 81, 93, 133, 141, 169, 177, 185, 213, 225, 257, 265, 269, 289, 301, 317, 353, 357, 361, 377, 397, 441, 445, 449, 485, 489, 509, 533, 537, 553, 565, 577, 581, 625, 653, 669, 685, 729, 749, 785, 817, 829, 837, 841, 905, 929, 933, 949, 961, 969, 993, 1005} (mod 1012).

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

k:=253; [p: p in PrimesUpTo(3000) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 2016

Mathematica

QuadPrimes2[1, 0, 253, 10000] (* see A106856 *)