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A141193
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Primes of the form -3*x^2+3*x*y+4*y^2 (as well as of the form 6*x^2+9*x*y+y^2).
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7
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7, 19, 43, 61, 73, 139, 157, 163, 199, 229, 271, 277, 283, 313, 349, 367, 397, 457, 463, 499, 541, 571, 577, 613, 619, 631, 643, 691, 709, 727, 733, 739, 757, 769, 823, 853, 859, 883, 919, 937, 967, 997, 1033, 1051, 1069, 1087, 1201, 1213, 1279, 1297, 1303, 1327, 1423, 1429
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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 = 19 and primes p = 1 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(2)=19 because we can write 19=-3*1^2+3*1*2+4*2^2
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MATHEMATICA
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Select[Prime[Range[250]], # == 19 || MatchQ[Mod[#, 57], Alternatives[1, 4, 7, 16, 25, 28, 43, 49, 55]]&] (* 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 24 2008
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STATUS
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approved
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