

A106932


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


2



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
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OFFSET

1,1


COMMENTS

Discriminant=67.
Different from A191041: 151 decomposes in Q(sqrt(67)) since 151 = ((1+3*sqrt(67))/2) * ((13*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



