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A056874 Primes of form x^2+xy+3y^2, discriminant -11. 10

%I

%S 3,5,11,23,31,37,47,53,59,67,71,89,97,103,113,137,157,163,179,181,191,

%T 199,223,229,251,257,269,311,313,317,331,353,367,379,383,389,397,401,

%U 419,421,433,443,449,463,467,487,499,509,521,577,587,599

%N Primes of form x^2+xy+3y^2, discriminant -11.

%C Also, primes of form (x^2+11*y^2)/4.

%C Also, primes of the form x^2-xy+3y^2 with x and y nonnegative. - _T. D. Noe_, May 07 2005

%C Primes congruent to 0, 1, 3, 4, 5 or 9 (mod 11). As this discriminant has class number 1, all binary quadratic forms ax^2+bxy+cy^2 with b^2-4ac=-11 represent these primes. - _Rick L. Shepherd_, Jul 25 2014

%C Also, primes which are squares (mod 11) (or, (mod 22), cf. A191020). - _M. F. Hasler_, Jan 15 2016

%C Also, primes p such that Legendre(-11,p) = 0 or 1. - _N. J. A. Sloane_, Dec 25 2017

%H Vincenzo Librandi, N. J. A. Sloane and Ray Chandler, <a href="/A056874/b056874.txt">Table of n, a(n) for n = 1..10000</a> [First 1000 terms from Vincenzo Librandi, next 4000 terms from N. J. A. Sloane]

%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)

%t QuadPrimes2[1, 1, 3, 100000] (* see A106856 *)

%o (PARI)

%o { fc2(a,b,c,M) = my(p,t1,t2,n);

%o m = 0;

%o for(n=1,M, p = prime(n);

%o t2 = qfbsolve(Qfb(a,b,c),p); if(t2 == 0,, m++; print(m," ",p )));

%o }

%o fc2(1,-1,3,10703);

%Y Cf. A002346 and A002347 for values of x and y.

%Y Primes in A028954.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Sep 02 2000

%E Edited by _N. J. A. Sloane_, Jun 01 2014 and Jun 16 2014

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Last modified January 15 18:58 EST 2019. Contains 319170 sequences. (Running on oeis4.)