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A049251
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Smallest nonnegative value taken on by 12x^2 - ny^2 for an infinite number of integer pairs (x, y).
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0
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3, 4, 0, 8, 3, 6, 5, 4, 3, 2, 1, 0, 12, 12, 12, 12, 3, 12, 12, 12, 3, 12, 1, 12, 3, 4, 0, 12, 3, 12, 12, 12, 3, 12, 12, 12, 11, 10, 9, 8, 3, 6, 5, 4, 3, 2, 1, 0, 12, 12, 12, 12, 3, 12, 5, 12, 3, 2, 1, 12, 12, 12, 12, 12, 3, 12, 5, 12, 3, 12, 1, 12, 3, 4, 0, 12, 3, 12, 12, 12, 3, 12, 1, 12
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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p = 12; f[n_, z_] := FindInstance[x > 0 && y > 0 && p*x^2 - n*y^2 == z, {x, y}, Integers, 1]; a[n_] := For[z = 0, z <= p, z = z + GCD[n, p], fz = TimeConstrained[f[n, z], 300]; fz = If[fz === $Aborted, {{x -> Null, y -> Null}}, fz]; If[fz =!= {}, Print["a(", n, ") = ", z, " {x, y} = ", {x, y} /. fz[[1]]]; Return[z]]]; Table[a[n], {n, 1, 84}] (* Jean-François Alcover, Oct 11 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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STATUS
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approved
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