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Search: id:A141184
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| A141184 |
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Primes of the form x^2+5*x*y-5*y^2 (as well as of the form x^2+7*x*y+y^2). |
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+0
7
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| 19, 31, 61, 79, 109, 139, 151, 181, 199, 211, 229, 241, 271, 331, 349, 379, 409, 421, 439, 499, 541, 571, 601, 619, 631, 661, 691, 709, 739, 751, 769, 811, 829, 859, 919, 991
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OFFSET
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1,1
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COMMENT
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Discriminant = 45. 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
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REFERENCES
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Borevich and Shafaewich, Number Theory.
D. B. Zagier, Zetafunktionen und quadratische Koerper.
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EXAMPLE
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a(1)=19 because we can write 19=3^2+5*3*1-5*1^2 (or 19=1^2+7*1*2+2^2).
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CROSSREFS
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Cf. A141185 (d=45), A033212 (Primes of form x^2+15*y^2.) A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).
Adjacent sequences: A141181 A141182 A141183 this_sequence A141185 A141186 A141187
Sequence in context: A117065 A006035 A104485 this_sequence A033212 A104227 A032743
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KEYWORD
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nonn
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AUTHOR
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Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 12 2008
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