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Search: id:A141373
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| A141373 |
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Primes of the form 4*x^2+4*x*y-5*y^2 (as well as of the form 4*x^2+12*x*y+3*y^2). |
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4
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| 3, 19, 43, 67, 139, 163, 211, 283, 307, 331, 379, 499, 523, 547, 571, 619, 643, 691, 739, 787, 811, 859, 883, 907
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Discriminant = 96. Class = 4. 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(2)=19 because we can write 19=4*2^2+4*2*1-5*1^2 (or 19=4*1^2+12*1*1+3*1^2).
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CROSSREFS
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Cf. A141374, A141375, A141376 (d=96).
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),
A141336, A141337 (d=92),
A141338, A141339 (d=93),
A141161, A141162, A141163 (d=148),
A141164, A141165, A141166 (d=229),
A141167, A141167, A141167 (d=257).
Sequence in context: A042371 A141644 A141170 this_sequence A107154 A031393 A146672
Adjacent sequences: A141370 A141371 A141372 this_sequence A141374 A141375 A141376
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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 28 2008
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