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Search: id:A141215
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| A141215 |
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Primes of the form 3*x^2+5*x*y-3*y^2 (as well as 5*x^2+9*x*y+y^2). |
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6
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| 3, 5, 13, 19, 41, 47, 61, 73, 83, 97, 103, 107, 109, 113, 127, 131, 137, 149, 163, 167, 179, 197, 199, 229, 239, 241, 257, 263, 269, 271, 283, 293, 317, 347, 353, 367, 379, 431, 439, 443, 449, 461, 463, 479, 487, 491, 503, 563, 569, 571, 601, 607, 613, 619
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OFFSET
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1,1
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COMMENT
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Discriminant = 61. Class = 1. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1
A subsequence of (and may possibly coincide with) A038941. - R. J. Mathar, Jul 22 2008
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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(8)=73 because we can write 73= 3*4^2+5*4*5-3*5^2 (or 73=5*3^2+9*3*1+1^2).
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CROSSREFS
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Cf. A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).
Sequence in context: A081353 A024820 A038941 this_sequence A106915 A112928 A106916
Adjacent sequences: A141212 A141213 A141214 this_sequence A141216 A141217 A141218
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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 (sergarmor(AT)yahoo.es), Jun 14 2008
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