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Decimal expansion of least x>0 satisfying 4*x^2+2*x+1=tan(x).
2

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

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

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

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

%N Decimal expansion of least x>0 satisfying 4*x^2+2*x+1=tan(x).

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

%e x=1.493485164079552774155578768915057065360164326614396...

%t a = 4; b = 2; 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, 1.4, 1.5}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200416 *)

%Y Cf. A200338.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 18 2011