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Search: id:A141174
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| A141174 |
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Primes of the form x^2+4*x*y-4*y^2 (as well as of the form x^2+6*x*y+y^2). |
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+0
8
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| 17, 41, 73, 89, 97, 113, 137, 193, 233, 241, 257, 281, 313, 337, 353, 401, 409, 433, 449, 457, 521, 569, 577, 593, 601, 617, 641, 673, 761, 769, 809, 857, 881, 929, 937, 953, 977
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OFFSET
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1,1
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COMMENT
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Discriminant = 32. 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
Values of the quadratic form are {0,1,4} mod 8, so this is a subset of A007519. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 30 2008
Is this the same sequence as A007519?
Contribution from Tito Piezas III (tpiezas(AT)gmail.com), Dec 28 2008: (Start)
Being a subset of A141131, this is also a subset of the primes of form u^2-2v^2. (End)
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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)=17 because we can write 17=3^2+4*3*1-4*1^2 (or 17=1^2+6*1*2+2^2)
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CROSSREFS
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Cf. A141175 (d=32), A007519 (Primes of form 8n+1.) A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).
Sequence in context: A126790 A089200 A004625 this_sequence A007519 A163185 A138005
Adjacent sequences: A141171 A141172 A141173 this_sequence A141175 A141176 A141177
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KEYWORD
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nonn,more
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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 (oscfalgan(AT)yahoo.es), Jun 12 2008
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