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Search: id:A141112
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| A141112 |
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Primes of the form 2*x^2+5*x*y-5*y^2 (as well as of the form 7*x^2+11*x*y+2*y^2). |
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55
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| 2, 5, 7, 13, 37, 47, 67, 73, 83, 97, 137, 163, 167, 193, 197, 223, 227, 293, 307, 317, 353, 383, 397, 457, 463, 487, 557, 577, 587, 593, 613, 617, 643, 683, 733, 743, 773, 787, 827, 853, 863, 877, 947, 967, 977, 983
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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(4)=37 because we can write 37=2*6^2+5*6*7-5*7^2 (or 37=7*1^2+11*1*2+2*2^2)
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CROSSREFS
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Cf. A141111.
Sequence in context: A119839 A107057 A038945 this_sequence A053647 A023242 A164570
Adjacent sequences: A141109 A141110 A141111 this_sequence A141113 A141114 A141115
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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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