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A056874
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Primes of form x^2+xy+3y^2, discriminant -11.
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11
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3, 5, 11, 23, 31, 37, 47, 53, 59, 67, 71, 89, 97, 103, 113, 137, 157, 163, 179, 181, 191, 199, 223, 229, 251, 257, 269, 311, 313, 317, 331, 353, 367, 379, 383, 389, 397, 401, 419, 421, 433, 443, 449, 463, 467, 487, 499, 509, 521, 577, 587, 599
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OFFSET
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1,1
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COMMENTS
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Also, primes of form (x^2+11*y^2)/4.
Also, primes of the form x^2-xy+3y^2 with x and y nonnegative. - T. D. Noe, May 07 2005
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
Also, primes which are squares (mod 11) (or, (mod 22), cf. A191020). - M. F. Hasler, Jan 15 2016
Also, primes p such that Legendre(-11,p) = 0 or 1. - N. J. A. Sloane, Dec 25 2017
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LINKS
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Vincenzo Librandi, N. J. A. Sloane and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi, next 4000 terms from N. J. A. Sloane]
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MATHEMATICA
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QuadPrimes2[1, 1, 3, 100000] (* see A106856 *)
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PROG
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(PARI)
{ fc2(a, b, c, M) = my(p, t1, t2, n);
m = 0;
for(n=1, M, p = prime(n);
t2 = qfbsolve(Qfb(a, b, c), p); if(t2 == 0, , m++; print(m, " ", p )));
}
fc2(1, -1, 3, 10703);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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