A139648 Primes of the form x^2 + 165*y^2.

181, 229, 421, 661, 709, 829, 1021, 1321, 1489, 1549, 1609, 1621, 1741, 2029, 2161, 2269, 2281, 2341, 2689, 3001, 3061, 3169, 3301, 3469, 3529, 4129, 4261, 4621, 4789, 4801, 4909, 5281, 5449, 5569, 5581, 5641, 5701, 6121, 6229, 6301, 6361

Offset: 1

Author

T. D. Noe, Apr 29 2008

Keywords

• nonn
• easy

Comments

Discriminant = -660.

The primes are congruent to {1, 49, 169, 181, 229, 289, 301, 361, 421, 529} (mod 660).

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(7000) | p mod 660 in {1, 49, 169, 181, 229, 289, 301, 361, 421, 529}]; // Vincenzo Librandi, Jul 28 2012

Magma

k:=165; [p: p in PrimesUpTo(7000) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 2016

Mathematica

QuadPrimes2[1, 0, 165, 10000] (* see A106856 *)