A106930 Primes of the form x^2 - xy + 16y^2, with x and y nonnegative.

67, 79, 127, 163, 277, 373, 421, 463, 541, 547, 571, 613, 631, 739, 823, 877, 967, 1009, 1033, 1051, 1087, 1093, 1129, 1213, 1297, 1579, 1621, 1663, 1723, 1831, 1933, 1999, 2011, 2179, 2251, 2269, 2293, 2377, 2389, 2437, 2503, 2557, 2683, 2689, 2731, 2767

Offset

1,1

Comments

Discriminant = -63.

This appears to coincide with the sequence of primes of the form x^2 + 63y^2. - Artur Jasinski, Apr 24 2008

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)

Mathematica

QuadPrimes2[1, -1, 16, 10000] (* see A106856 *)

Prog

(PARI) {a(n)= local(m, c, x); if(n<1, 0, c=0; m=1; while( c<n, m++; if( isprime(m), for(x=0, sqrtint(m\7), if(issquare(m-7*x^2), if( x%3==0, c++); break)))); m)} /* Michael Somos, May 28 2005 */

Crossrefs

Sequence in context: A044035 A124476 A066475 * A106929 A173040 A091490

Adjacent sequences: A106927 A106928 A106929 * A106931 A106932 A106933

Keyword

nonn,easy

Author

T. D. Noe, May 09 2005

Status

approved