|
| |
|
|
A141168
|
|
Primes of the form 4*x^2+9*x*y-11*y^2.
|
|
5
| |
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
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
| Borevich and Shafaewich, Number Theory
D. B. Zagier, Zetafunktionen und quadratische Koerper
|
|
|
LINKS
| Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000
|
|
|
EXAMPLE
| a(5)=23 because we can write 23= 4*2^2+9*2*1-11*1^2
|
|
|
CROSSREFS
| Cf. A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65). A141167 (d=257).
Sequence in context: A119449 A137977 A160950 * A079132 A184802 A023257
Adjacent sequences: A141165 A141166 A141167 * A141169 A141170 A141171
|
|
|
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
|
| |
|
|
