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Search: id:A141111
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| A141111 |
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Primes of the form 4*x^2+x*y-4*y^2 (as well as of the form 4*x^2+9*x*y+y^2). |
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55
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| 29, 61, 79, 101, 131, 139, 179, 181, 191, 199, 211, 251, 269, 311, 389, 419, 439, 491, 521, 569, 571, 599, 601, 641, 659, 701, 719, 751, 809, 829, 859, 881, 911, 919, 971, 991
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OFFSET
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1,1
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COMMENT
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Discriminant = 65. Class = 2. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and 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)=79 because we can write 79=4*5^2+5*3-4*3^2 (or 79=4*2^2+9*2*3+3^2)
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CROSSREFS
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Cf. A141112.
Sequence in context: A042678 A042680 A132770 this_sequence A122114 A142047 A046275
Adjacent sequences: A141108 A141109 A141110 this_sequence A141112 A141113 A141114
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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 04 2008, Jun 05 2008
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