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A049247
Smallest nonnegative value taken on by 8x^2 - ny^2 for an infinite number of integer pairs (x, y).
0
4, 0, 5, 4, 3, 2, 1, 0, 8, 8, 8, 8, 8, 2, 8, 8, 4, 0, 8, 8, 8, 2, 1, 8, 7, 6, 5, 4, 3, 2, 1, 0, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 5, 8, 8, 2, 1, 8, 4, 0, 8, 8, 3, 2, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 7, 6, 5, 4, 3, 2, 1, 0, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 5, 8, 8, 2, 8, 8, 8, 8, 8, 4, 8, 2, 8, 8, 4, 0, 8, 8, 3, 2, 1, 8, 8
OFFSET
1,1
MATHEMATICA
p = 8; 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], Which[n == 49, z = 4; fz = $Aborted, n == 81, z = 8; fz = $Aborted, n == 83, z = 5; fz = $Aborted, n == 101, z = 3; fz = $Aborted, True, 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, 105}] (* Jean-François Alcover, Oct 11 2016 *)
CROSSREFS
Sequence in context: A201196 A019906 A197251 * A175621 A016578 A268631
KEYWORD
nonn
STATUS
approved