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A200633 Decimal expansion of the lesser of two values of x satisfying 6*x^2 - 1 = tan(x) and 0 < x < Pi/2.

%I A200633 #10 Jan 30 2025 13:18:29
%S A200633 5,0,9,7,4,1,7,0,8,9,1,8,5,4,8,4,8,9,2,4,6,0,4,9,6,6,5,8,5,2,5,8,6,8,
%T A200633 6,2,7,0,8,3,1,7,8,6,0,0,8,3,0,9,5,8,7,7,8,7,4,7,1,7,9,9,7,5,2,7,3,3,
%U A200633 5,2,6,3,9,7,6,8,4,6,6,8,7,4,2,1,8,0,2,1,7,9,8,8,3,0,5,1,3,4,9
%N A200633 Decimal expansion of the lesser of two values of x satisfying 6*x^2 - 1 = tan(x) and 0 < x < Pi/2.
%C A200633 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200633 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200633 lesser:  0.50974170891854848924604966585258686270831...
%e A200633 greater: 1.48978365608349822096681798686067147504261...
%t A200633 a = 6; c = 1;
%t A200633 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200633 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200633 r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
%t A200633 RealDigits[r]   (* A200633 *)
%t A200633 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A200633 RealDigits[r]   (* A200634 *)
%Y A200633 Cf. A200614.
%K A200633 nonn,cons
%O A200633 0,1
%A A200633 _Clark Kimberling_, Nov 20 2011