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Decimal expansion of least x>0 satisfying 5*x^2+3=tan(x).
2

%I #8 Feb 07 2025 16:44:07

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

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

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

%N Decimal expansion of least x>0 satisfying 5*x^2+3=tan(x).

%C See A200614 for a guide to related sequences. The Mathematica program includes a graph.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e x=1.500794081535079381882252476557571752326596214...

%t a = 5; c = -3;

%t f[x_] := a*x^2 - 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, 1.5, 1.51}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200630 *)

%Y Cf. A200338.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 20 2011