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A200617 Decimal expansion of the greater of two values of x satisfying 4*x^2 - 1 = tan(x) and 0 < x < Pi/2.

%I A200617 #12 Jan 30 2025 12:18:16
%S A200617 1,4,3,3,0,6,8,7,8,5,5,8,4,9,1,6,8,7,5,2,2,6,7,8,2,7,1,7,5,9,6,7,2,8,
%T A200617 7,7,0,2,2,0,9,2,4,0,2,6,8,4,7,5,6,2,1,5,0,8,5,0,2,2,7,6,3,4,2,5,3,1,
%U A200617 1,6,8,1,0,4,7,6,9,2,5,0,7,4,5,8,6,3,1,9,1,6,5,0,3,1,8,1,0,5,9
%N A200617 Decimal expansion of the greater of two values of x satisfying 4*x^2 - 1 = tan(x) and 0 < x < Pi/2.
%C A200617 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200617 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200617 lesser:  0.839582259045302941513764008863804986308...
%e A200617 greater: 1.350956593976519397744696294368524715373...
%t A200617 a = 4; c = 1;
%t A200617 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200617 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200617 r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]
%t A200617 RealDigits[r]   (* A200616 *)
%t A200617 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A200617 RealDigits[r]   (* A200617 *)
%Y A200617 Cf. A200614, A200616.
%K A200617 nonn,cons
%O A200617 1,2
%A A200617 _Clark Kimberling_, Nov 20 2011