A139658 Primes of the form x^2 + 345*y^2.

349, 409, 541, 601, 829, 1021, 1129, 1381, 1429, 1549, 1669, 1741, 1789, 2221, 2281, 2341, 2749, 3049, 3061, 3109, 3121, 3169, 3229, 3301, 3361, 3709, 3889, 4129, 4261, 4441, 4549, 4861, 4969, 5101, 5521, 5569, 5641, 5689, 5821, 5869

Offset: 1

Author

T. D. Noe, Apr 29 2008

Keywords

• nonn
• easy

Comments

Discriminant = -1380. See A139643 for more information.

The primes are congruent to {1, 49, 121, 169, 289, 301, 349, 361, 409, 469, 541, 601, 721, 829, 841, 901, 949, 961, 1021, 1129, 1189, 1369} (mod 1380).

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 1380 in {1, 49, 121, 169, 289, 301, 349, 361, 409, 469, 541, 601, 721, 829, 841, 901, 949, 961, 1021, 1129, 1189, 1369}]; // Vincenzo Librandi, Jul 29 2012

Magma

k:=345; [p: p in PrimesUpTo(6000) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 2016

Mathematica

QuadPrimes2[1, 0, 345, 10000] (* see A106856 *)