A196402 - OEIS

%I #6 Mar 30 2012 18:57:50

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

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

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

%N Decimal expansion of the least positive number x satisfying e^(-x)=2*cos(x).

%e x=1.45367366646104161868434356812734006445958806...

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

%t t = x /. FindRoot[E^(-x) == Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100];

%t RealDigits[t]  (* A196401 *)

%t t = x /. FindRoot[E^(-x) == 2 Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100]; RealDigits[t]  (* A196402 *)

%t t = x /. FindRoot[E^(-x) == 3 Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100]; RealDigits[t]  (* A196403 *)

%t t = x /. FindRoot[E^(-x) == 4 Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100]; RealDigits[t]  (* A196404 *)

%t t = x /. FindRoot[E^(-x) == 5 Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100]; RealDigits[t]  (* A196405 *)

%t t = x /. FindRoot[E^(-x) == 6 Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100]; RealDigits[t]  (* A196406 *)

%Y Cf. A196401.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 02 2011