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Search: id:A141778
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| A141778 |
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Primes of the form 4*x^2+3*x*y-5*y^2 (as well as of the form 8*x^2+11*x*y+y^2). |
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2
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| 2, 5, 11, 17, 47, 53, 67, 71, 73, 79, 89, 97, 107, 109, 131, 139, 157, 167, 173, 179, 199, 223, 227, 233, 251, 257, 263, 269, 271, 277, 283, 307, 311, 317, 331, 347, 367, 373, 401, 409, 443, 449, 461, 463, 467, 479, 487, 509, 523, 587, 601, 607, 613, 619, 631
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Discriminant = 89. 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
Is this the same as A038977? - R. J. Mathar, Jul 04 2008
A subsequence of (and may possibly coincide with) A038977. - 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(1)=2 because we can write 2= 4*1^2+3*1*1-5*1^2
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CROSSREFS
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See also A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141158 (d=20). A141159, A141160 (d=21). A141170, A141171 (d=24). A141172, A141173 (d=28). A141174, A141175 (d=32). A141176, A141177 (d=33). A141178 (d=37). A141179, A141180 (d=40). A141181 (d=41). A141182, A141183 (d=44). A141184, A141185 (d=45). A141122, A141187 (d=48). A141188 (d=52). A141189 (d=53). A141190, A141191 (d=56). A141192, A141193 (d=57). A141301, A141302, A141303, A141304 (d=60). A141215 (d=61). A141111, A141112 (d=65). A141750 (d=73). A141772, A141773 (d=85). A141776, A141777 (d=88). A141778 (d=89). A141161, A141162, A141163 (d=148). A141164, A141165, A141166 (d=229). A141167, A141168, A141169 (d=257).
Sequence in context: A126204 A091936 A038977 this_sequence A117877 A025200 A132455
Adjacent sequences: A141775 A141776 A141777 this_sequence A141779 A141780 A141781
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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), Jul 04 2008
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