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A113975
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Devil's Farey: coefficient expansion of a quadratic over quadratic that has 123 roots and a Farey p[1/2]=1 ( correction).
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0
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2, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6
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OFFSET
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0,1
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COMMENTS
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I call it the devil's Farey because of the 6,6,6 structure. I was trying to get an integer root quadratic over quadratic that had the Farey conditions: p[1/2]=1;p[0]=0;p[1]=0
The function has the characteristic Farey shape: fa[x_] := 1/p[x] /; 0 <= x <= 1/2 fa[x_] := p[x] /; 1/2 < x <= 1.
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LINKS
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FORMULA
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b(n)= coefficient expansion of 1 + 2/x - 6/(1 - x) a(n) = b(n)
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MATHEMATICA
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a = 1; b = 2; c = 3; d = 3; e = 0; f = -1 p[x_] = FullSimplify[ExpandAll[(x - a)*(x - b)*(x - c)/((x - d)*(x - e)*(x -f))]] a = Abs[ReplacePart[Table[Abs[Coefficient[Series[p[x], {x, 0, 30}], x^n]], {n, -1, 30}], -5, 2]]
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CROSSREFS
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KEYWORD
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nonn,uned
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AUTHOR
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STATUS
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approved
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