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A200620 Decimal expansion of the lesser of two values of x satisfying 5*x^2 - 1 = tan(x) and 0 < x < Pi/2.

%I A200620 #13 Jan 30 2025 12:18:13
%S A200620 5,7,3,8,2,5,6,1,4,2,2,0,7,0,7,5,1,9,4,7,0,6,9,9,3,0,7,3,9,5,0,2,8,9,
%T A200620 7,2,0,4,0,0,1,2,6,2,0,5,6,7,5,7,0,8,3,3,8,2,7,1,3,0,1,2,7,4,1,8,7,9,
%U A200620 3,4,4,0,9,7,0,1,7,1,2,2,0,9,2,8,2,1,3,3,5,3,7,0,0,6,1,5,4,5,0
%N A200620 Decimal expansion of the lesser of two values of x satisfying 5*x^2 - 1 = tan(x) and 0 < x < Pi/2.
%C A200620 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200620 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200620 lesser:  0.5738256142207075194706993073950289720400...
%e A200620 greater: 1.469002719513610613223362597583632411278000...
%t A200620 a = 5; c = 1;
%t A200620 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200620 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200620 r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
%t A200620 RealDigits[r]   (* A200620 *)
%t A200620 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A200620 RealDigits[r]   (* A200621 *)
%Y A200620 Cf. A200614, A200621.
%K A200620 nonn,cons
%O A200620 0,1
%A A200620 _Clark Kimberling_, Nov 20 2011