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A200623 Decimal expansion of the greater of two values of x satisfying 5*x^2 - 2 = tan(x) and 0 < x < Pi/2.

%I A200623 #10 Jan 30 2025 13:16:59
%S A200623 1,4,5,4,7,9,9,2,1,3,5,1,9,9,9,5,5,2,6,3,7,0,7,8,4,3,0,0,7,9,8,9,4,4,
%T A200623 5,8,9,0,1,2,6,0,8,7,1,2,0,1,7,0,7,4,3,1,5,0,0,2,1,9,3,2,6,9,3,9,2,3,
%U A200623 5,3,2,2,1,5,8,0,0,0,6,1,6,9,5,4,5,8,6,7,0,2,0,8,8,7,6,7,1,9,2
%N A200623 Decimal expansion of the greater of two values of x satisfying 5*x^2 - 2 = tan(x) and 0 < x < Pi/2.
%C A200623 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200623 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200623 lesser:  0.770896883914277182837264927358706321868754...
%e A200623 greater: 1.4547992135199955263707843007989445890126087...
%t A200623 a = 5; c = 2;
%t A200623 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200623 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200623 r = x /. FindRoot[f[x] == g[x], {x, .7, .8}, WorkingPrecision -> 110]
%t A200623 RealDigits[r]    (* A200622 *)
%t A200623 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A200623 RealDigits[r]   (* A200623 *)
%Y A200623 Cf. A200614.
%K A200623 nonn,cons
%O A200623 1,2
%A A200623 _Clark Kimberling_, Nov 20 2011