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Search: id:A141785
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| A141785 |
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Primes of the form -x^2+5*x*y+5*y^2 (as well as of the form 9*x^2+15*x*y+5*y^2). |
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+0
1
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| 5, 11, 29, 41, 59, 71, 89, 101, 131, 149, 179, 191, 239, 251, 269, 281, 311, 359, 389, 401, 419, 431, 449, 461, 479, 491, 509, 521, 569, 599, 641, 659, 701, 719, 761, 809, 821, 839, 881, 911, 929, 941, 971
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OFFSET
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1,1
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COMMENT
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Discriminant = 45. 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(2)=29 because we can write 29=-1^2+5*1*2+5*2^2 (or 29=9*1^2+15*1*1+5*1^2)
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CROSSREFS
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Cf. A141184 (d=45) A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).
Sequence in context: A141561 A019345 A049489 this_sequence A144311 A074367 A088486
Adjacent sequences: A141782 A141783 A141784 this_sequence A141786 A141787 A141788
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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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