A196397 - OEIS

%I #5 Mar 30 2012 18:57:50

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

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

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

%N Decimal expansion of the positive number x satisfying e^x=3*cos(x).

%e x=0.768578540894330492996861582141419667498497324350...

%t Plot[{E^x, 2 Cos[x], 3 Cos[x], 4 Cos[x]}, {x, 0, Pi/2}]

%t t = x /.

%t   FindRoot[E^x == 2 Cos[x], {x, .5, .6}, WorkingPrecision -> 100]; RealDigits[t]  (* A196396 *)

%t t = x /.

%t   FindRoot[E^x == 3 Cos[x], {x, .7, .8}, WorkingPrecision -> 100]; RealDigits[t]  (* A196397 *)

%t t = x /.

%t   FindRoot[E^x == 4 Cos[x], {x, .8, 1.0}, WorkingPrecision -> 100]; RealDigits[t]  (* A196398 *)

%t t = x /.

%t   FindRoot[E^x == 5 Cos[x], {x, .8, 1.0}, WorkingPrecision -> 100]; RealDigits[t]  (* A196399 *)

%t t = x /.

%t   FindRoot[E^x == 6 Cos[x], {x, 1.0, 1.1}, WorkingPrecision -> 100]; RealDigits[t]  (* A196400 *)

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 02 2011