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Decimal expansion of least x satisfying 9*x^2 = sec(x) and 0 < x < Pi.
3

%I #8 Apr 10 2021 02:06:36

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

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

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

%N Decimal expansion of least x satisfying 9*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: 0.3435193844487517285157937916054768...

%e greatest: 1.52286717667793005738690747334562...

%t a = 9; 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, .3, .4}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201420 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201421 *)

%Y Cf. A201397.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Dec 02 2011