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A200615 Decimal expansion of the greater of two values of x satisfying 3*x^2 - 1 = tan(x) and 0 < x < Pi/2.

%I A200615 #10 Jan 30 2025 12:14:37
%S A200615 1,3,5,0,9,5,6,5,9,3,9,7,6,5,1,9,3,9,7,7,4,4,6,9,6,2,9,4,3,6,8,5,2,4,
%T A200615 7,1,5,3,7,3,0,3,7,3,0,1,6,7,5,8,8,2,5,6,2,9,7,8,8,4,4,6,2,0,4,7,6,6,
%U A200615 0,1,7,1,8,4,6,3,4,3,8,0,2,8,2,8,5,3,9,6,5,0,6,3,4,5,9,4,4,0,6
%N A200615 Decimal expansion of the greater of two values of x satisfying 3*x^2 - 1 = tan(x) and 0 < x < Pi/2.
%C A200615 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200615 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200615 lesser:  0.839582259045302941513764008863804986308...
%e A200615 greater: 1.350956593976519397744696294368524715373...
%t A200615 a = 3; c = 1;
%t A200615 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200615 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200615 r = x /. FindRoot[f[x] == g[x], {x, .8, .9}, WorkingPrecision -> 110]
%t A200615 RealDigits[r]   (* A200614 *)
%t A200615 r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
%t A200615 RealDigits[r]   (* A200615 *)
%Y A200615 Cf. A200338.
%K A200615 nonn,cons
%O A200615 1,2
%A A200615 _Clark Kimberling_, Nov 20 2011