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

%I #6 Feb 07 2025 16:44:07

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

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

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

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

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

%e x=1.45439713056258019365396314995213521786510471954...

%t a = 4; b = -2; c = 3;

%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] (* A200605 *)

%Y Cf. A200338.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 19 2011