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A200681 Decimal expansion of the lesser of two values of x satisfying 3*x^2 = tan(x) and 0 < x < Pi/2.

%I A200681 #10 Jan 30 2025 13:35:37
%S A200681 3,4,7,4,2,5,7,6,4,4,7,7,4,3,8,7,1,1,2,8,9,0,5,6,4,1,2,9,5,5,3,2,5,8,
%T A200681 7,6,7,2,3,1,5,3,1,7,0,2,7,7,1,9,3,9,3,7,2,0,4,8,9,6,8,3,6,8,0,0,8,0,
%U A200681 9,5,6,5,4,2,5,1,2,3,4,8,8,8,2,7,0,5,2,9,2,2,7,5,0,5,7,8,8,1,3
%N A200681 Decimal expansion of the lesser of two values of x satisfying 3*x^2 = tan(x) and 0 < x < Pi/2.
%C A200681 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200681 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200681 lesser:  0.34742576447743871128905641295532587...
%e A200681 greater: 1.40306042080937123884892134944944201...
%t A200681 a = 3; c = 0;
%t A200681 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200681 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200681 r = x /. FindRoot[f[x] == g[x], {x, .3, .4}, WorkingPrecision -> 110]
%t A200681 RealDigits[r] (* A200681 *)
%t A200681 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A200681 RealDigits[r] (* A200682 *)
%Y A200681 Cf. A200614.
%K A200681 nonn,cons
%O A200681 0,1
%A A200681 _Clark Kimberling_, Nov 20 2011