

A056874


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


11



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

1,1


COMMENTS

Also, primes of form (x^2+11*y^2)/4.
Also, primes of the form x^2xy+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^24ac=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


LINKS

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]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)


MATHEMATICA

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


PROG

(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);


CROSSREFS

Cf. A002346 and A002347 for values of x and y.
Primes in A028954.
Sequence in context: A023202 A049436 A117010 * A280773 A109927 A146276
Adjacent sequences: A056871 A056872 A056873 * A056875 A056876 A056877


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Sep 02 2000


EXTENSIONS

Edited by N. J. A. Sloane, Jun 01 2014 and Jun 16 2014


STATUS

approved



