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A200593 Decimal expansion of least x>0 satisfying 3*x^2-3*x+1=tan(x). 2

%I #5 Mar 30 2012 18:58:01

%S 3,2,7,2,8,3,7,3,0,1,5,9,5,3,0,8,4,1,1,5,6,0,0,1,1,4,3,3,8,4,3,2,4,7,

%T 7,4,4,0,7,6,1,9,1,3,4,2,5,1,4,3,2,3,6,6,4,6,6,6,9,2,4,4,1,4,4,1,8,9,

%U 4,1,5,5,8,3,2,9,6,4,6,7,4,6,8,5,0,9,3,4,1,7,7,6,4,6,3,5,0,4,3

%N Decimal expansion of least x>0 satisfying 3*x^2-3*x+1=tan(x).

%C See A200338 for a guide to related sequences. The Mathematica program includes a graph.

%e x=0.3272837301595308411560011433843247744076191342...

%t a = 3; b = -3; c = 1;

%t f[x_] := a*x^2 + b*x + c; g[x_] := Tan[x]

%t Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200593 *)

%Y Cf. A200338.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 19 2011

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