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

%I #33 May 24 2022 02:42:54

%S 17,19,23,29,37,47,59,71,73,83,89,103,107,127,131,149,157,163,167,173,

%T 181,193,199,211,223,227,241,257,263,277,283,293,307,317,349,359,389,

%U 397,431,439,449,457,461,467,479,491,509,523,557,569,571,601,613,617

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

%C Discriminant = -67.

%C 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

%H Ray Chandler, <a href="/A106932/b106932.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Vincenzo Librandi)

%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)

%H <a href="/index/Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</a>

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

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 09 2005

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Last modified April 25 07:41 EDT 2024. Contains 371964 sequences. (Running on oeis4.)