A106932 Primes of the form x^2 + xy + 17y^2, with x and y nonnegative.

17, 19, 23, 29, 37, 47, 59, 71, 73, 83, 89, 103, 107, 127, 131, 149, 157, 163, 167, 173, 181, 193, 199, 211, 223, 227, 241, 257, 263, 277, 283, 293, 307, 317, 349, 359, 389, 397, 431, 439, 449, 457, 461, 467, 479, 491, 509, 523, 557, 569, 571, 601, 613, 617

Offset

1,1

Comments

Discriminant = -67.

Different from A191041: 151 decomposes in Q(sqrt(-67)) since 151 = ((1 + 3*sqrt(-67))/2) * ((1 - 3*sqrt(-67))/2); nevertheless, x^2 + xy + 17y^2 = 151 has no nonnegative solution. - Jianing Song, Feb 19 2021

Links

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)

Index to sequences related to decomposition of primes in quadratic fields

Mathematica

QuadPrimes2[1, 1, 17, 10000] (* see A106856 *)

Crossrefs

Sequence in context: A187372 A106933 A191041 * A007635 A140947 A205700

Adjacent sequences: A106929 A106930 A106931 * A106933 A106934 A106935

Keyword

nonn,easy

Author

T. D. Noe, May 09 2005

Status

approved