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Search: id:A141190
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| A141190 |
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Primes of the form 2*x^2+4*x*y-5*y^2 (as well as of the form 2*x^2+8*x*y+y^2). |
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7
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| 2, 11, 43, 67, 107, 113, 137, 163, 179, 193, 211, 233, 281, 331, 337, 347, 379, 401, 443, 449, 457, 491, 499, 547, 569, 571, 617, 641, 659, 673, 683, 739, 809, 827, 883, 907, 947, 953, 977
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OFFSET
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1,1
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COMMENT
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Discriminant = 56. 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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D. B. Zagier, Zetafunktionen und quadratische Koerper.
Borevich and Shafaewich, Number Theory.
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EXAMPLE
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a(3)=43 because we can write 43=2*4^2+4*4*1-5*1^2 (or 43=2*3^2+8*3*1+1^2)
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CROSSREFS
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Cf. A141191 (d=56) A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).
Adjacent sequences: A141187 A141188 A141189 this_sequence A141191 A141192 A141193
Sequence in context: A140322 A027247 A128241 this_sequence A048500 A050620 A027253
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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 (marcanmar(AT)alum.us.es), Jun 12 2008
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