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A141191
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Primes of the form -2*x^2+4*x*y+5*y^2 (as well as of the form 10*x^2+16*x*y+5*y^2).
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6
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5, 7, 13, 31, 47, 61, 101, 103, 157, 167, 173, 181, 199, 223, 229, 269, 271, 293, 311, 349, 367, 383, 397, 439, 461, 479, 503, 509, 607, 647, 661, 677, 719, 727, 733, 773, 797, 829, 839, 853, 887, 941, 983, 997, 1013, 1021, 1039, 1063, 1069, 1109, 1151, 1181
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OFFSET
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1,1
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COMMENTS
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Discriminant = 56. 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.
Also primes of the form -x^2+6xy+5y^2. cf. A243187.
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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(4)=31 because we can write 31=-2*7^2+4*7*3+5*3^2 (or 31=10*1^2+16*1*1+5*1^2).
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MATHEMATICA
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Reap[For[p = 2, p < 2000, p = NextPrime[p], If[FindInstance[p == -2*x^2 + 4*x*y + 5*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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For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.
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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 (lourdescm84(AT)hotmail.com), Jun 12 2008
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EXTENSIONS
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STATUS
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approved
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