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Search: id:A141131
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| A141131 |
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Primes of the form x^2+2*x*y-y^2. |
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+0
51
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| 2, 7, 17, 23, 31, 41, 47, 71, 73, 79, 89, 97, 103, 113, 127, 137, 151, 167, 191, 193, 199, 223, 233, 239, 241, 257, 263, 271, 281, 311, 313, 337, 353, 359, 367, 383, 401, 409, 431, 433, 439, 449, 457, 463, 479, 487, 503, 521, 569, 577, 593, 599, 601, 607, 617
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Discriminant = 8. 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
Values of the quadratic form are {0,1,2,4,6,7} mod 8, so this is a subset of A038873. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 30 2008
Is this the same sequence as A038873?
Contribution from Tito Piezas III (tpiezas(AT)gmail.com), Dec 28 2008: (Start)
Also primes of form u^2-2v^2. The transformation {u,v}={x+y,y} yields the form in the title.
(End)
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REFERENCES
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D. B. Zagier, Zetafunktionen und quadratische Koerper.
Borevich and Shafaewich, Number Theory.
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EXAMPLE
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a(2)=7 because we can write 7=2^2+2*2*1-1^2
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MATHEMATICA
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lst={}; Do[Do[p=x^2+2*x*y-y^2; If[PrimeQ[p]&&p>1, AppendTo[lst, p]], {x, y+1, 2*5!}], {y, 2*5!}]; Union[lst] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 30 2009]
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CROSSREFS
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Cf. A141111, A141112 (d=65).
Sequence in context: A074884 A105911 A038873 this_sequence A049594 A049590 A049570
Adjacent sequences: A141128 A141129 A141130 this_sequence A141132 A141133 A141134
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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 06 2008
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