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Decimal expansion of least x satisfying 10*x^2 - 1 = sec(x) and 0 < x < Pi.
3

%I #8 Apr 09 2021 19:16:09

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

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

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

%N Decimal expansion of least x satisfying 10*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: 0.4600006985794904216969349833844460938634...

%e greatest: 1.52590577141056614542926620695066975318...

%t a = 10; 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] (* A201529 *)

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

%t RealDigits[r] (* A201530 *)

%Y Cf. A201397.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Dec 02 2011