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Search: id:A141158
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| A141158 |
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Primes of the form x^2+4*x*y-y^2. |
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+0
19
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| 5, 11, 19, 29, 31, 41, 59, 61, 71, 79, 89, 101, 109, 131, 139, 149, 151, 179, 181, 191, 199, 211, 229, 239, 241, 251, 269, 271, 281, 311, 331, 349, 359, 379, 389, 401, 409, 419, 421, 431, 439, 449, 461, 479, 491, 499, 509, 521, 541, 569, 571, 599, 601, 619
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Discriminant = 20. 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 {0,1,4} mod 5, so this is a subset of A038872. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 30 2008
Is this the same sequence as A038872?
Contribution from Tito Piezas III (tpiezas(AT)gmail.com), Dec 28 2008: (Start)
Also primes of the form u^2-5v^2. The transformation {u,v}={x+2y,y} transforms it into the one in the title.
(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(3)=19 because we can write 19=2^2+4*2*5-5^2
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CROSSREFS
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Cf. A038872 (Primes congruent to {0, 1, 4} mod 5. ) A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).
Sequence in context: A132087 A089270 A038872 this_sequence A130828 A108151 A088059
Adjacent sequences: A141155 A141156 A141157 this_sequence A141159 A141160 A141161
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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 (oscfalgan(AT)yahoo.es), Jun 12 2008
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