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Search: id:A141123
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| A141123 |
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Primes of the form -x^2+2*x*y+2*y^2 (as well as of the form 3*x^2+6*x*y+2*y^2). |
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49
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| 2, 3, 11, 23, 47, 59, 71, 83, 107, 131, 167, 179, 191, 227, 239, 251, 263, 311, 347, 359, 383, 419, 431, 443, 467, 479, 491, 503, 563, 587, 599, 647, 659, 683, 719, 743, 827, 839, 863, 887, 911, 947, 971, 983
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OFFSET
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1,1
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COMMENT
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Discriminant = 12. 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
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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(3)=11 because we can write 11=-1^2+2*1*2+2*2^2 (or 11=3*1^2+6*1*1+2*1^2)
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CROSSREFS
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Cf. A141122 (d=12), A068231 (Primes congruent to 11 (mod 12)) A141111, A141112 (d=65).
Sequence in context: A158017 A091310 A040994 this_sequence A119641 A074496 A065849
Adjacent sequences: A141120 A141121 A141122 this_sequence A141124 A141125 A141126
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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 05 2008
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