A106950 Primes of the form x^2 + 18y^2.

19, 43, 67, 73, 97, 139, 163, 193, 211, 241, 283, 307, 313, 331, 337, 379, 409, 433, 457, 499, 523, 547, 571, 577, 601, 619, 643, 673, 691, 739, 769, 787, 811, 859, 883, 907, 937, 1009, 1033, 1051, 1123, 1129, 1153, 1171, 1201, 1249, 1291, 1297, 1321

Offset: 1

Author

T. D. Noe, May 09 2005

Keywords

• nonn
• easy

Comments

Discriminant = -72.

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(2000) | p mod 24 in {1, 19} ]; // Vincenzo Librandi, Jul 22 2012

Mathematica

QuadPrimes2[1, 0, 18, 10000] (* see A106856 *)

PARI

{a(n)= my(m, c); if(n<1, 0, c=0; m=0; while( cMichael Somos, Aug 19 2006 */

Formula

Primes congruent to 1,19 modulo 24. - Michael Somos, Aug 19 2006