A201412 - OEIS

%I #8 Apr 10 2021 08:06:33

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

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

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

%N Decimal expansion of least x satisfying 5*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:  0.474127690420775415934748938569551538434...

%e greatest: 1.4792710652904107931042853415537602633...

%t a = 5; 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, .4, .5}, WorkingPrecision -> 110]

%t RealDigits[r]     (* A201412 *)

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

%t RealDigits[r]    (* A201413 *)

%Y Cf. A201397.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Dec 01 2011