A201415 - OEIS

%I #10 Nov 26 2024 21:07:43

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

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

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

%N Decimal expansion of greatest x satisfying 6*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:  0.42800895010041097002739347769069180659...

%e greatest: 1.496285048607652953479229041712424469...

%t a = 6; 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, .4, .5}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A201414 *)

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

%t RealDigits[r]    (* A201415 *)

%o (PARI) solve(x=1,2, 6*x^2*cos(x)-1) \\ _Charles R Greathouse IV_, Nov 26 2024

%Y Cf. A201397.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Dec 01 2011