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A141168
Primes of the form 4*x^2+9*x*y-11*y^2.
7
2, 11, 13, 17, 23, 29, 31, 59, 73, 79, 89, 137, 139, 173, 199, 211, 223, 239, 283, 293, 307, 317, 349, 373, 379, 397, 401, 433, 457, 479, 491, 503, 523, 563, 571, 593, 613, 647, 673, 683, 701, 709, 719, 727, 769, 773, 787, 797, 829, 839, 887, 911, 967
OFFSET
1,1
COMMENTS
Discriminant = 257. Class = 3. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1
Also primes represented by the improperly equivalent form 11*x^2+9*x*y-4*y^2. - Juan Arias-de-Reyna, Mar 18 2011
REFERENCES
Z. I. Borevich and I. R. Shafarevich, Number Theory
LINKS
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014.
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.
EXAMPLE
a(5)=23 because we can write 23= 4*2^2+9*2*1-11*1^2
CROSSREFS
Cf. A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65). A141167 (d=257).
For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.
Sequence in context: A137977 A338976 A160950 * A259394 A079132 A184802
KEYWORD
nonn
AUTHOR
Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (sergarmor(AT)yahoo.es), Jun 12 2008
STATUS
approved