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A141302
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Primes of the form -x^2+6*x*y+6*y^2 (as well as of the form 11*x^2+18*x*y+6*y^2).
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10
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11, 59, 71, 131, 179, 191, 239, 251, 311, 359, 419, 431, 479, 491, 599, 659, 719, 839, 911, 971, 1019, 1031, 1091, 1151, 1259, 1319, 1439, 1451, 1499, 1511, 1559, 1571, 1619, 1811, 1871, 1931, 1979, 2039, 2099, 2111, 2339, 2351, 2399, 2411, 2459, 2531, 2579, 2591, 2699, 2711
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OFFSET
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1,1
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COMMENTS
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Discriminant = 60. 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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Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966.
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.
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LINKS
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EXAMPLE
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a(3)=71 because we can write 71=-1^2+6*1*3+6*3^2 (or 71=11*1^2+18*1*2+6*2^2).
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MATHEMATICA
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Reap[For[p = 2, p < 3000, p = NextPrime[p], If[FindInstance[p == -x^2 + 6*x*y + 6*y^2, {x, y}, Integers, 1] =!= {}, Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Oct 25 2016 *)
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CROSSREFS
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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 24 2008
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EXTENSIONS
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STATUS
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approved
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