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A200636 Decimal expansion of the greater of two values of x satisfying 6*x^2 - 5 = tan(x) and 0 < x < Pi/2.

%I A200636 #10 Jan 30 2025 13:20:07
%S A200636 1,4,3,5,9,7,2,7,9,7,7,4,7,7,2,7,8,3,9,7,3,7,7,5,9,5,7,1,3,6,3,1,8,0,
%T A200636 6,3,4,7,5,2,4,1,9,4,0,1,6,2,8,5,6,2,7,2,5,4,8,4,5,2,6,7,0,5,9,8,1,8,
%U A200636 9,4,9,9,2,6,7,0,0,1,3,6,4,5,6,5,8,9,7,8,0,1,1,3,5,1,5,1,5,6,9
%N A200636 Decimal expansion of the greater of two values of x satisfying 6*x^2 - 5 = tan(x) and 0 < x < Pi/2.
%C A200636 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200636 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200636 lesser:  1.0650216206187079002949359361195227...
%e A200636 greater: 1.4359727977477278397377595713631806...
%t A200636 a = 6; c = 5;
%t A200636 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200636 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200636 r = x /. FindRoot[f[x] == g[x], {x, 1, 1.1}, WorkingPrecision -> 110]
%t A200636 RealDigits[r]   (* A200635 *)
%t A200636 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A200636 RealDigits[r]   (* A200636 *)
%Y A200636 Cf. A200614.
%K A200636 nonn,cons
%O A200636 1,2
%A A200636 _Clark Kimberling_, Nov 20 2011