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Search: id:A141160
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| A141160 |
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Primes of the form -x^2+3*x*y+3*y^2 (as well as of the form 5*x^2+9*x*y+3*y^2). |
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+0
7
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| 3, 5, 17, 41, 47, 59, 83, 89, 101, 131, 167, 173, 227, 251, 257, 269, 293, 311, 353, 383, 419, 461, 467, 479, 503, 509, 521, 563, 587, 593, 647, 677, 719, 761, 773, 797, 839, 857, 881, 887, 929, 941, 971, 983
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OFFSET
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1,1
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COMMENT
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Discriminant = 21. 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)=17 because we can write 17=-1^2+3*1*2+3*2^2 (or
17=5*1^2+9*1*1+3*1^2)
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CROSSREFS
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Cf. A141159 (d=21) A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).
Sequence in context: A148520 A148521 A148522 this_sequence A113275 A001572 A131342
Adjacent sequences: A141157 A141158 A141159 this_sequence A141161 A141162 A141163
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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 (marcanmar(AT)alum.us.es), Jun 12 2008
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