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Decimal expansion of least x satisfying 9*x^2 - 1 = sec(x) and 0 < x < Pi.
3

%I #8 Apr 09 2021 19:05:41

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

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

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

%N Decimal expansion of least x satisfying 9*x^2 - 1 = sec(x) and 0 < x < Pi.

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

%e least: 0.4866365134428287964150106888774053061...

%e greatest: 1.52027247650615034595984357679438306...

%t a = 9; c = -1;

%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] (* A201527 *)

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

%t RealDigits[r] (* A201528 *)

%Y Cf. A201397.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Dec 02 2011