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A200611 Decimal expansion of least x > 0 satisfying 4*x^2 - 4*x + 3 = tan(x).

%I A200611 #12 Aug 05 2018 08:25:41
%S A200611 1,3,7,6,0,5,2,5,1,5,3,9,9,6,6,9,7,5,3,5,7,9,4,8,9,2,7,4,8,8,0,9,1,1,
%T A200611 6,1,2,8,3,1,1,3,8,8,8,2,4,0,3,0,3,6,7,6,5,9,3,2,9,8,6,3,0,8,3,2,5,3,
%U A200611 6,4,7,0,0,9,9,4,9,9,1,6,0,5,7,3,2,2,6,6,0,7,3,2,0,7,1,8,9,3,7
%N A200611 Decimal expansion of least x > 0 satisfying 4*x^2 - 4*x + 3 = tan(x).
%C A200611 See A200338 for a guide to related sequences. The Mathematica program includes a graph.
%H A200611 G. C. Greubel, <a href="/A200611/b200611.txt">Table of n, a(n) for n = 1..10000</a>
%e A200611 1.3760525153996697535794892748809116128311...
%t A200611 a = 4; b = -4; c = 3;
%t A200611 f[x_] := a*x^2 + b*x + c; g[x_] := Tan[x]
%t A200611 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200611 r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
%t A200611 RealDigits[r]   (* A200611 *)
%o A200611 (PARI) solve(x=1, 3/2, 4*x^2 - 4*x + 3 - tan(x)) \\ _Michel Marcus_, Aug 05 2018
%Y A200611 Cf. A200338.
%K A200611 nonn,cons
%O A200611 1,2
%A A200611 _Clark Kimberling_, Nov 19 2011