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A140002 Primes of the form 8*x^2 + 165*y^2. 1

%I

%S 173,197,293,557,677,1493,1613,1733,1877,1997,2213,2477,2837,3533,

%T 3797,4133,4157,4253,4373,4397,4517,4637,5477,5573,5693,5717,6173,

%U 7013,7757,7853,8093,8117,8597,9173,9413,9437,9533,9677,10133,10733

%N Primes of the form 8*x^2 + 165*y^2.

%C Discriminant = -5280. See A139827 for more information.

%H Vincenzo Librandi and Ray Chandler, <a href="/A140002/b140002.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)

%F The primes are congruent to {173, 197, 293, 413, 437, 557, 677, 893, 1157, 1253} (mod 1320).

%t QuadPrimes2[8, 0, 165, 10000] (* see A106856 *)

%o (PARI) isA140002(n) = if(isprime(n),{r=0;for(y=0,floor(sqrt(n/165)),t=n-165*y^2;if((t%8==0)&(issquare(t/8)),r=1));r},0) \\ _Michael B. Porter_, Oct 05 2009

%o (MAGMA) [p: p in PrimesUpTo(12000) | p mod 1320 in [173, 197, 293, 413, 437, 557, 677, 893, 1157, 1253]]; // _Vincenzo Librandi_, Aug 04 2012

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 02 2008

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Last modified January 29 01:42 EST 2020. Contains 331328 sequences. (Running on oeis4.)