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Decimal expansion of least x>0 satisfying x^2-2x+4=tan(x).
2

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

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

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

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

%N Decimal expansion of least x>0 satisfying x^2-2x+4=tan(x).

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

%e x=1.2554456489217720608319765072175592705503777...

%t a = 1; b = -2; c = 4;

%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, 1.2, 1.3}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200484 *)

%Y Cf. A200338.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 18 2011