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

Author

T. D. Noe, May 09 2005

Keywords

• nonn
• easy

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

Programs

Mathematica

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