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Search: id:A142957
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| A142957 |
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Primes of the form 3*x^2+5*x*y-6*y^2 (as well as of the form 6*x^2+11*x*y+y^2). |
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+0
1
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| 2, 3, 11, 31, 43, 47, 53, 61, 73, 79, 89, 97, 101, 103, 109, 113, 151, 163, 167, 191, 193, 197, 227, 229, 241, 269, 283, 293, 307, 313, 353, 379, 389, 397, 419, 421, 431, 449, 461, 463, 467, 479, 487, 491, 503, 509, 521, 547, 557, 571, 593, 607, 613, 617, 631
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OFFSET
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1,1
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COMMENT
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Discriminant = 97. Class = 1. 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(6)=47 because we can write 47=3*11^2+5*11*(-4)-6*(-4)^2 (or 47=6*2^2+11*2*1+1^2).
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CROSSREFS
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Cf. A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).
Sequence in context: A003455 A103275 A038987 this_sequence A080155 A032357 A144056
Adjacent sequences: A142954 A142955 A142956 this_sequence A142958 A142959 A142960
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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 (laucabfer(AT)alum.us.es), Jul 17 2008
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