A002347 -id:A002347 - cp's OEIS frontend

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

Offset: 1

N. J. A. Sloane, Sep 02 2000

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

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)

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

Primes in A028954.

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

{ 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);

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

A002346 Consider all primes of form p = (x^2 + 11y^2 )/4; sequence gives values of x.

Original entry on oeis.org

1, 3, 0, 9, 5, 7, 12, 6, 15, 13, 3, 9, 17, 4, 21, 3, 23, 16, 21, 25, 15, 20, 1, 5, 27, 18, 30, 12, 19, 27, 35, 9, 37, 25, 39, 15, 2, 30, 24, 10, 29, 21, 39, 31, 3, 43, 40, 45, 15, 47, 48, 36, 42, 1, 7, 45, 41, 27, 51, 13, 24, 17, 19, 51, 53, 23, 38, 54, 3, 49, 29, 45

Offset: 1

N. J. A. Sloane

nonn

A. J. C. Cunningham, Quadratic Partitions. Hodgson, London, 1904, p. 1.
D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 55.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A. J. C. Cunningham, Quadratic Partitions, Hodgson, London, 1904 [Annotated scans of selected pages]

Cf. A002347, A056874.

Offset corrected by Mohammed Yaseen, Jul 24 2023

cp's OEIS Frontend

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

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