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A200622 Decimal expansion of the lesser of two values of x satisfying 5*x^2 - 2 = tan(x) and 0 < x < Pi/2.

%I A200622 #10 Jan 30 2025 13:16:57
%S A200622 7,7,0,8,9,6,8,8,3,9,1,4,2,7,7,1,8,2,8,3,7,2,6,4,9,2,7,3,5,8,7,0,6,3,
%T A200622 2,1,8,6,8,7,5,4,8,4,3,3,6,1,9,2,8,8,8,3,4,1,1,0,9,3,2,0,8,9,6,3,2,6,
%U A200622 1,7,9,1,3,9,9,0,3,8,2,1,8,6,6,4,7,7,7,3,0,9,1,9,7,1,1,5,9,8,7
%N A200622 Decimal expansion of the lesser of two values of x satisfying 5*x^2 - 2 = tan(x) and 0 < x < Pi/2.
%C A200622 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200622 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200622 lesser:  0.770896883914277182837264927358706321868754...
%e A200622 greater: 1.454799213519995526370784300798944589012608...
%t A200622 a = 5; c = 2;
%t A200622 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200622 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200622 r = x /. FindRoot[f[x] == g[x], {x, .7, .8}, WorkingPrecision -> 110]
%t A200622 RealDigits[r]   (* A200622 *)
%t A200622 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A200622 RealDigits[r]   (* A200623 *)
%Y A200622 Cf. A200614.
%K A200622 nonn,cons
%O A200622 0,1
%A A200622 _Clark Kimberling_, Nov 20 2011