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A200390 Decimal expansion of least x>0 satisfying 3*x^2+x+4=tan(x). 2

%I #5 Mar 30 2012 18:58:00

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

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

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

%N Decimal expansion of least x>0 satisfying 3*x^2+x+4=tan(x).

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

%e x=1.48858415458687138966616452928986405228828970200...

%t a = 3; b = 1; 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, 1.4, 1.5}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200390 *)

%Y Cf. A200338.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 17 2011

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