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%I #10 Apr 09 2021 14:57:35
%S 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,
%T 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,
%U 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
%N Decimal expansion of the number x satisfying 0 < x < 2*Pi and 2x = (1 + x^2)*tan(x).
%e x=0.7682171553153782504312122866979254095466915658...
%t Plot[{1/(1 + x^2), 0.874*Cos[x]}, {x, .5, 1}]
%t t = x /. FindRoot[Tan[x] == 2 x/(1 + x^2), {x, .5, 1}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196913 *)
%t c = N[Sqrt[t^4 + 6 t^2 + 1]/(t^4 + 2 t^2 + 1), 100]
%t RealDigits[c] (* A196914 *)
%t slope = N[-c*Sin[t], 100]
%t RealDigits[slope](* A196915 *)
%Y Cf. A196816, A196914.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 07 2011
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