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Search: id:A141750
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| A141750 |
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Primes of the form 4*x^2+3*x*y-4*y^2 (as well as of the form 2*x^2+9*x*y+y^2). |
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4
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| 2, 3, 19, 23, 37, 41, 61, 67, 71, 73, 79, 89, 97, 109, 127, 137, 149, 173, 181, 211, 223, 227, 251, 257, 269, 283, 293, 311, 317, 347, 349, 353, 359, 367, 373, 383, 389, 397, 401, 419, 439, 457, 461, 463, 479, 487, 499, 503, 509, 523, 547, 557, 587, 593, 607
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Discriminant = 73. 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 A038957? - R. J. Mathar, Jul 04 2008
A subsequence of (and may possibly coincide with) A038957. - 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(2)=3 because we can write 3= 4*1^2+3*1*1-4*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). A141161, A141162, A141163 (d=148). A141164, A141165, A141166 (d=229). A141167, A141168, A141169 (d=257).
Sequence in context: A128353 A109418 A038957 this_sequence A090476 A127941 A140555
Adjacent sequences: A141747 A141748 A141749 this_sequence A141751 A141752 A141753
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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 03 2008
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