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A200621 Decimal expansion of the greater of two values of x satisfying 5*x^2 - 1 = tan(x) and 0 < x < Pi/2.

%I A200621 #10 Jan 30 2025 12:18:09
%S A200621 1,4,6,9,0,0,2,7,1,9,5,1,3,6,1,0,6,1,3,2,2,3,3,6,2,5,9,7,5,8,3,6,3,2,
%T A200621 4,1,1,2,7,8,0,0,0,3,4,6,1,5,3,5,7,4,6,4,8,5,8,8,7,7,3,5,8,6,2,2,8,1,
%U A200621 7,2,0,1,8,4,8,3,0,6,1,0,4,5,6,4,2,4,9,0,1,9,0,6,6,9,7,6,7,0,9
%N A200621 Decimal expansion of the greater of two values of x satisfying 5*x^2 - 1 = tan(x) and 0 < x < Pi/2.
%C A200621 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200621 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200621 lesser:  0.5738256142207075194706993073950289720400...
%e A200621 greater: 1.469002719513610613223362597583632411278000...
%t A200621 a = 5; c = 1;
%t A200621 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200621 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200621 r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
%t A200621 RealDigits[r]   (* A200620 *)
%t A200621 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A200621 RealDigits[r]   (* A200621 *)
%Y A200621 Cf. A200614.
%K A200621 nonn,cons
%O A200621 1,2
%A A200621 _Clark Kimberling_, Nov 20 2011