login
Decimal expansion of greatest x satisfying 4*x^2 - 1 = sec(x) and 0 < x < Pi.
3

%I #11 Jan 30 2025 15:40:27

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

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

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

%N Decimal expansion of greatest x satisfying 4*x^2 - 1 = sec(x) and 0 < x < Pi.

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

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e least: 0.774427257079893623257029009000...

%e greatest: 1.4313635500690391357640449937...

%t a = 4; 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, .7, .8}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201517 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201518 *)

%Y Cf. A201397.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Dec 02 2011