A200611 - OEIS

%I #12 Aug 05 2018 08:25:41

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

%C See A200338 for a guide to related sequences. The Mathematica program includes a graph.

%H G. C. Greubel, <a href="/A200611/b200611.txt">Table of n, a(n) for n = 1..10000</a>

%e 1.3760525153996697535794892748809116128311...

%t a = 4; b = -4; c = 3;

%t f[x_] := a*x^2 + b*x + c; g[x_] := Tan[x]

%t Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200611 *)

%o (PARI) solve(x=1, 3/2, 4*x^2 - 4*x + 3 - tan(x)) \\ _Michel Marcus_, Aug 05 2018

%Y Cf. A200338.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 19 2011