A201408 - OEIS

%I #8 Apr 10 2021 08:06:05

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

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

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

%N Decimal expansion of least x satisfying 3*x^2 = sec(x) and 0 < x < Pi.

%C See A201397 for a guide to related sequences. The Mathematica program includes a graph.

%e least:  0.6461374540628972972901679159101125226952859...

%e greatest: 1.39986411944606406722963950518361037394178...

%t a = 3; c = 0;

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A201408 *)

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

%t RealDigits[r]    (* A201409 *)

%Y Cf. A201397.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Dec 01 2011