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A200679 Decimal expansion of the lesser of two values of x satisfying 2*x^2 = tan(x) and 0 < x < Pi/2.

%I A200679 #11 Jan 30 2025 13:21:12
%S A200679 5,5,9,7,0,4,1,5,2,2,7,3,0,8,0,6,5,0,6,1,0,3,7,7,2,1,2,8,3,5,8,8,0,2,
%T A200679 2,9,6,9,7,4,6,8,1,6,7,1,2,6,5,9,3,6,9,3,1,3,4,8,7,3,7,8,2,6,9,0,2,3,
%U A200679 0,0,6,6,4,1,2,7,2,9,0,3,8,0,8,3,0,1,0,8,7,4,2,3,3,0,6,4,0,2,1
%N A200679 Decimal expansion of the lesser of two values of x satisfying 2*x^2 = tan(x) and 0 < x < Pi/2.
%C A200679 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200679 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200679 lesser:  0.55970415227308065061037721283588022...
%e A200679 greater: 1.27034264779958271106399033503202112...
%t A200679 a = 2; c = 0;
%t A200679 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200679 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200679 r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
%t A200679 RealDigits[r] (* A200679 *)
%t A200679 r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
%t A200679 RealDigits[r] (* A200680 *)
%Y A200679 Cf. A200614.
%K A200679 nonn,cons
%O A200679 0,1
%A A200679 _Clark Kimberling_, Nov 20 2011