|
%I #8 Apr 10 2021 02:06:55
%S 1,3,4,1,4,3,0,1,6,6,2,9,1,2,5,9,7,6,4,5,7,6,0,8,0,5,0,6,7,6,3,6,1,4,
%T 1,7,1,7,7,1,4,0,8,2,9,1,7,9,4,8,3,0,1,1,3,0,7,5,1,6,4,3,7,7,1,8,0,4,
%U 9,8,8,2,4,9,6,7,8,0,0,0,6,9,8,5,4,2,0,4,6,3,0,5,8,6,0,2,4,9,5
%N Decimal expansion of greatest 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 1,2
%A _Clark Kimberling_, Dec 02 2011
|
