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Search: id:A141188
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| A141188 |
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Primes of the form 3*x^2+2*x*y-4*y^2 (as well as of the form 3*x^2+8*x*y+y^2). |
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+0
6
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| 3, 13, 17, 23, 29, 43, 53, 61, 79, 101, 103, 107, 113, 127, 131, 139, 157, 173, 179, 181, 191, 199, 211, 233, 251, 257, 263, 269, 277, 283, 311, 313, 337, 347, 367, 373, 389, 419, 433, 439, 443, 467, 491, 503, 521, 523, 547, 563, 569, 571, 599, 601, 607, 641
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Contribution from Tito Piezas III (tpiezas(AT)gmail.com), Dec 28 2008: (Start)
Primes of the form u^2-13v^2. Using the transformation {u,v} = {4x+y,x} yields the second quadratic form in the title.
This is probably identical to A038883.
(End)
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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(9)=79 because we can write 79= 3*5^2+2*5*2-4*2^2 (or 79=3*3^2+8*3*2+2^2)
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MAPLE
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Discriminant = 52. 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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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: A038956 A040123 A038883 this_sequence A019347 A045433 A045434
Adjacent sequences: A141185 A141186 A141187 this_sequence A141189 A141190 A141191
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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 (sergarmor(AT)yahoo.es), Jun 12 2008
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