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A049239
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Smallest nonnegative value taken on by px^2-qy^2 for an infinite number of integer pairs (x,y), where (p,q) = (1,1), (1,2), (2,1), (1,3), (2,2), (3,1)...
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0
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0, 1, 1, 1, 0, 2, 0, 2, 1, 0, 1, 2, 0, 2, 1, 1, 2, 3, 1, 2, 2, 1, 2, 3, 0, 2, 4, 3, 1, 1, 3, 4, 1, 3, 5, 4, 0, 0, 3, 4, 0, 2, 1, 0, 0, 1, 2, 3, 1, 5, 1, 3, 5, 1, 1, 1, 2, 3, 4, 5, 0, 2, 4, 6, 2, 2, 1, 2, 2, 0, 5, 6, 1, 3, 0, 7, 1, 3, 1, 2, 1, 4, 5, 6, 0, 2, 1, 4, 8, 4, 1, 1, 2, 0, 1, 5, 6, 7, 1, 3, 5, 7, 0, 2, 5
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OFFSET
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1,6
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LINKS
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EXAMPLE
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Array begins:
0, 1, 1, 0, 1, ...
1, 0, 2, 2, 2, ...
2, 1, 0, 3, 3, ...
0, 2, 1, 0, 4, ...
1, 2, 2, 1, 0, ...
...
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MATHEMATICA
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f[p_, q_, z_] := FindInstance[x > 0 && y > 0 && p*x^2 - q*y^2 == z, {x, y}, Integers, 1]; a[p_, q_] := For[z = 0, True, z = z + GCD[p, q], fz = f[p, q, z]; If[fz =!= {}, Print["a(", p, " ", q, ") = ", z, " {x, y} = ", {x, y} /. fz[[1]]]; Return[z]]]; Table[TimeConstrained[a[p - q + 1, q], 300], {p, 1, 14}, {q, p, 1, -1}] // Flatten (* Jean-François Alcover, Oct 10 2016 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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