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

%I #9 Apr 10 2021 02:06:52

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

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

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

%N Decimal expansion of least x satisfying 3*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: 0.95353909754991468966727069537237822743...

%e greatest: 1.341430166291259764576080506763614171...

%t a = 3; 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, .9, 1}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201515 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.5}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201516 *)

%Y Cf. A201397.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Dec 02 2011