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

%I #8 Apr 09 2021 19:05:51

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

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

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

%N Decimal expansion of greatest 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 1,2

%A _Clark Kimberling_, Dec 02 2011