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A200680 Decimal expansion of the greater of two values of x satisfying 2*x^2 = tan(x) and 0 < x < Pi/2.

%I A200680 #10 Jan 30 2025 13:21:16
%S A200680 1,2,7,0,3,4,2,6,4,7,7,9,9,5,8,2,7,1,1,0,6,3,9,9,0,3,3,5,0,3,2,0,2,1,
%T A200680 1,2,5,1,4,7,6,9,7,3,1,0,4,6,2,8,0,7,5,6,5,6,7,6,2,5,4,0,1,2,7,6,5,4,
%U A200680 9,0,4,4,1,1,5,6,5,0,3,4,9,6,4,1,6,9,7,1,2,3,6,3,5,9,4,4,1,3,5
%N A200680 Decimal expansion of the greater of two values of x satisfying 2*x^2 = tan(x) and 0 < x < Pi/2.
%C A200680 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200680 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200680 lesser:  0.55970415227308065061037721283588022...
%e A200680 greater: 1.27034264779958271106399033503202112...
%t A200680 a = 2; c = 0;
%t A200680 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200680 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200680 r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
%t A200680 RealDigits[r] (* A200679 *)
%t A200680 r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
%t A200680 RealDigits[r] (* A200680 *)
%Y A200680 Cf. A200614.
%K A200680 nonn,cons
%O A200680 1,2
%A A200680 _Clark Kimberling_, Nov 20 2011