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

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

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

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

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

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

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

%e x=1.45114125891546019821987565757144529866649279...

%t a = 3; b = 0; c = 2;

%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] (* A200385 *)

%Y Cf. A200338.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 17 2011