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Search: id:A141173
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| A141173 |
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Primes of the form -2*x^2+2*x*y+3*y^2 (as well as of the form 6*x^2+10*x*y+3*y^2). |
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+0
7
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| 3, 7, 19, 31, 47, 59, 83, 103, 131, 139, 167, 199, 223, 227, 251, 271, 283, 307, 311, 367, 383, 419, 439, 467, 479, 503, 523, 563, 587, 607, 619, 643, 647, 691, 719, 727, 787, 811, 839, 859, 887, 971, 983
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OFFSET
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1,1
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COMMENT
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Discriminant = 28. 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(3)=19 because we can write 19=-2*4^2+2*4*3+3*3^2 (or 19=6*1^2+10*1*1+3*1^2)
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CROSSREFS
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Cf. A141172 (d=28) A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).
Adjacent sequences: A141170 A141171 A141172 this_sequence A141174 A141175 A141176
Sequence in context: A006032 A066148 A093932 this_sequence A077313 A102271 A112633
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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 (lourdescm84(AT)hotmail.com), Jun 12 2008
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