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Search: id:A141772
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| A141772 |
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Primes of the form 3*x^2+5*x*y-5*y^2 (as well as of the form 7*x^2+13*x*y+3*y^2). |
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3
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| 3, 5, 7, 17, 23, 37, 73, 97, 107, 113, 163, 167, 173, 193, 197, 227, 233, 277, 283, 313, 317, 337, 347, 367, 397, 487, 503, 547, 607, 617, 643, 653, 673, 677, 683, 743, 787, 823, 827, 853, 857, 877, 887, 907, 947, 983, 997
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OFFSET
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1,1
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COMMENT
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Discriminant = 85. 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(1)=3 because we can write 3= 3*1^2+5*1*0-5*0^2 (or 3=7*0^2+13*0*1+3*1^2
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CROSSREFS
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Cf. A141773 (d=85). 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). A141161, A141162, A141163 (d=148). A141164, A141165, A141166 (d=229). A141167, A141168, A141169 (d=257).
Sequence in context: A137258 A053341 A086086 this_sequence A032496 A002092 A057476
Adjacent sequences: A141769 A141770 A141771 this_sequence A141773 A141774 A141775
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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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