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A196913
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Decimal expansion of the number x satisfying 0<x<2*pi and 2x=(1+x^2)*tan(x).
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3
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7, 6, 8, 2, 1, 7, 1, 5, 5, 3, 1, 5, 3, 7, 8, 2, 5, 0, 4, 3, 1, 2, 1, 2, 2, 8, 6, 6, 9, 7, 9, 2, 5, 4, 0, 9, 5, 4, 6, 6, 9, 1, 5, 6, 5, 8, 5, 7, 1, 6, 3, 2, 1, 6, 7, 1, 9, 4, 9, 1, 6, 8, 4, 5, 8, 8, 1, 3, 4, 3, 5, 2, 8, 9, 3, 3, 1, 2, 0, 8, 9, 2, 5, 6, 2, 2, 8, 9, 9, 7, 6, 8, 7, 3, 7, 7, 1, 4, 2, 8
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OFFSET
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0,1
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LINKS
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Table of n, a(n) for n=0..99.
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EXAMPLE
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x=0.7682171553153782504312122866979254095466915658...
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MATHEMATICA
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Plot[{1/(1 + x^2), 0.874*Cos[x]}, {x, .5, 1}]
t = x /. FindRoot[Tan[x] == 2 x/(1 + x^2), {x, .5, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196913 *)
c = N[Sqrt[t^4 + 6 t^2 + 1]/(t^4 + 2 t^2 + 1), 100]
RealDigits[c] (* A196914 *)
slope = N[-c*Sin[t], 100]
RealDigits[slope](* A196915 *)
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CROSSREFS
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Cf. A196816, A196914.
Sequence in context: A202345 A010512 A195370 * A091343 A196397 A154170
Adjacent sequences: A196910 A196911 A196912 * A196914 A196915 A196916
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KEYWORD
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nonn,cons
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AUTHOR
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Clark Kimberling, Oct 07 2011
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STATUS
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approved
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