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A200616 Decimal expansion of the lesser of two values of x satisfying 4*x^2 - 1 = tan(x) and 0 < x < Pi/2.

%I A200616 #10 Jan 30 2025 12:18:18
%S A200616 6,6,9,1,0,2,9,7,2,0,2,3,5,7,5,4,1,6,0,7,6,6,0,1,2,5,0,1,8,8,4,5,6,9,
%T A200616 8,2,4,5,6,2,2,7,9,4,4,3,8,7,1,8,5,6,4,3,3,0,1,1,5,8,3,0,0,2,1,7,3,9,
%U A200616 4,9,8,4,0,8,4,2,6,3,7,2,4,5,6,0,2,7,9,3,9,0,4,3,4,2,2,9,3,7,4
%N A200616 Decimal expansion of the lesser of two values of x satisfying 4*x^2 - 1 = tan(x) and 0 < x < Pi/2.
%C A200616 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200616 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200616 lesser:  0.839582259045302941513764008863804986308...
%e A200616 greater: 1.350956593976519397744696294368524715373...
%t A200616 a = 4; c = 1;
%t A200616 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200616 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200616 r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]
%t A200616 RealDigits[r]   (* A200616 *)
%t A200616 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A200616 RealDigits[r]   (* A200617 *)
%Y A200616 Cf. A200614.
%K A200616 nonn,cons
%O A200616 0,1
%A A200616 _Clark Kimberling_, Nov 20 2011