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Search: id:A142955
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| A142955 |
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Primes of the form 3*x^2+4*x*y-5*y^2 (as well as of the form 3*x^2+10*x*y+2*y^2). |
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+0
2
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| 2, 3, 19, 31, 59, 67, 71, 79, 103, 107, 127, 151, 167, 179, 211, 223, 227, 307, 331, 379, 383, 431, 439, 487, 523, 547, 563, 599, 607, 659, 683, 743, 751, 787, 811, 827, 839, 863, 887, 907, 911, 971, 983, 991
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OFFSET
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1,1
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COMMENT
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Discriminant = 76. 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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Borevich and Shafaewich, Number Theory.
D. B. Zagier, Zetafunktionen und quadratische Koerper.
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EXAMPLE
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a(4)=31 because we can write 31=3*3^2+4*3*2-5*2^2 (or 31=3*1^2+10*1*2+2*2^2).
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CROSSREFS
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Cf. A142956 (d=76). A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).
Sequence in context: A140555 A058912 A040145 this_sequence A088790 A135958 A163665
Adjacent sequences: A142952 A142953 A142954 this_sequence A142956 A142957 A142958
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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 14 2008
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