A201421 - OEIS

%I #12 Jan 30 2025 15:38:48

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

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

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

%N Decimal expansion of greatest x satisfying 9*x^2 = 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:  0.3435193844487517285157937916054768...

%e greatest: 1.52286717667793005738690747334562...

%t a = 9; c = 0;

%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, .3, .4}, WorkingPrecision -> 110]

%t RealDigits[r]     (* A201420 *)

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

%t RealDigits[r]    (* A201421 *)

%Y Cf. A201397.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Dec 02 2011