A201292 - OEIS

%I #9 Apr 10 2021 21:32:15

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

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

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

%N Decimal expansion of x satisfying 3*x^2 + 1 = cot(x) and 0 < x < Pi.

%C See A201280 for a guide to related sequences. The Mathematica program includes a graph.

%e x=0.5110289688671886549895911481110493672...

%t a = 3; c = 1;

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A201292 *)

%Y Cf. A201280.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 29 2011