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A200635 Decimal expansion of the lesser of two values of x satisfying 6*x^2 - 5 = tan(x) and 0 < x < Pi/2.

%I A200635 #10 Jan 30 2025 13:20:18
%S A200635 1,0,6,5,0,2,1,6,2,0,6,1,8,7,0,7,9,0,0,2,9,4,9,3,5,9,3,6,1,1,9,5,2,2,
%T A200635 7,3,3,0,1,3,2,2,7,0,0,8,8,5,6,6,5,4,2,2,2,0,2,6,8,6,1,0,7,3,2,6,6,7,
%U A200635 7,2,0,2,9,0,1,1,1,2,4,3,0,9,1,0,0,6,8,5,2,3,6,7,9,8,8,5,9,6,4
%N A200635 Decimal expansion of the lesser of two values of x satisfying 6*x^2 - 5 = tan(x) and 0 < x < Pi/2.
%C A200635 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200635 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200635 lesser:  1.0650216206187079002949359361195227330132...
%e A200635 greater: 1.4359727977477278397377595713631806347524...
%t A200635 a = 6; c = 5;
%t A200635 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200635 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200635 r = x /. FindRoot[f[x] == g[x], {x, 1, 1.1}, WorkingPrecision -> 110]
%t A200635 RealDigits[r]   (* A200635 *)
%t A200635 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A200635 RealDigits[r]   (* A200636 *)
%Y A200635 Cf. A200614.
%K A200635 nonn,cons
%O A200635 1,3
%A A200635 _Clark Kimberling_, Nov 20 2011