A200682 - OEIS

%I #8 Apr 09 2021 15:53:32

%S 1,4,0,3,0,6,0,4,2,0,8,0,9,3,7,1,2,3,8,8,4,8,9,2,1,3,4,9,4,4,9,4,4,2,

%T 0,1,5,7,1,2,9,3,1,3,8,4,2,4,5,1,1,1,4,6,8,9,5,9,4,8,8,5,9,1,8,5,2,9,

%U 0,1,7,3,9,6,5,1,5,1,1,0,2,5,2,8,1,8,7,6,3,1,0,6,4,1,3,8,5,0,6

%N Decimal expansion of the greater of two values of x satisfying 3*x^2 = tan(x) and 0 < x < Pi/2.

%C See A200614 for a guide to related sequences. The Mathematica program includes a graph.

%e lesser:  0.34742576447743871128905641295532587...

%e greater: 1.40306042080937123884892134944944201...

%t a = 3; c = 0;

%t f[x_] := a*x^2 - 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, .3, .4}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200681 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200682 *)

%Y Cf. A200614.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 20 2011