|
Search: id:A141159
|
|
|
| A141159 |
|
Primes of the form x^2+3*x*y-3*y^2 (as well as of the form x^2+5*x*y+y^2). |
|
+0
7
|
|
| 7, 37, 43, 67, 79, 109, 127, 151, 163, 193, 211, 277, 331, 337, 373, 379, 421, 457, 463, 487, 499, 541, 547, 571, 613, 631, 673, 709, 739, 751, 757, 823, 877, 883, 907, 919, 967, 991
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Discriminant = 21. Class = 2. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1
|
|
REFERENCES
|
Borevich and Shafaewich, Number Theory.
D. B. Zagier, Zetafunktionen und quadratische Koerper.
|
|
EXAMPLE
|
a(1)=7 because we can write 7=2^2+3*2*1-3*1^2 (or
7=1^2+5*1*1+1^2).
|
|
CROSSREFS
|
Cf. A141160 (d=21), A139492 (Primes of the form x^2 + 5x*y + y^2 for x and y nonnegative) A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).
Sequence in context: A043374 A038478 A043010 this_sequence A139492 A092475 A106924
Adjacent sequences: A141156 A141157 A141158 this_sequence A141160 A141161 A141162
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (laucabfer(AT)alum.us.es), Jun 12 2008
|
|
|
Search completed in 0.004 seconds
|
