A200633 - OEIS

A200633

Decimal expansion of the lesser of two values of x satisfying 6*x^2 - 1 = tan(x) and 0 < x < Pi/2.

%I #10 Jan 30 2025 13:18:29

%S 5,0,9,7,4,1,7,0,8,9,1,8,5,4,8,4,8,9,2,4,6,0,4,9,6,6,5,8,5,2,5,8,6,8,

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

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

%N Decimal expansion of the lesser of two values of x satisfying 6*x^2 - 1 = tan(x) and 0 < x < Pi/2.

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

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e lesser: 0.50974170891854848924604966585258686270831...

%e greater: 1.48978365608349822096681798686067147504261...

%t a = 6; c = 1;

%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, .5, .6}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200633 *)

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

%t RealDigits[r] (* A200634 *)

%Y Cf. A200614.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 20 2011