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A141192
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Primes of the form 3*x^2+3*x*y-4*y^2 (as well as of the form 8*x^2+11*x*y+2*y^2).
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7
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2, 3, 29, 41, 53, 59, 71, 89, 107, 113, 167, 173, 179, 227, 257, 269, 281, 293, 317, 383, 401, 431, 449, 509, 521, 563, 569, 599, 641, 659, 677, 683, 743, 773, 797, 827, 839, 857, 863, 887, 911, 941, 953, 971, 977, 983, 1019, 1091, 1097, 1181, 1193, 1229, 1283, 1307, 1319
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OFFSET
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1,1
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COMMENTS
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Discriminant = 57. 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
p = 3 and primes p = 2 mod 3 such that 57 is a square mod p. - Juan Arias-de-Reyna, Mar 20 2011
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REFERENCES
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Z. I. Borevich and I. R. Shafarevich, Number Theory.
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LINKS
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EXAMPLE
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a(6)=59 because we can write 59=3*7^2+3*7*8-4*8^2 (or 59=8*1^2+11*1*3+2*3^2)
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MATHEMATICA
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Select[Prime[Range[250]], # == 3 || MatchQ[Mod[#, 57], Alternatives[2, 8, 14, 29, 32, 41, 50, 53, 56]]&] (* Jean-François Alcover, Oct 28 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 (oscfalgan(AT)yahoo.es), Jun 12 2008
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STATUS
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approved
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