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Decimal expansion of the least positive number x satisfying e^(-x)=4*sin(x).
5

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

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

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

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

%N Decimal expansion of the least positive number x satisfying e^(-x)=4*sin(x).

%e x=0.205080044539291644456051290893472362476208209177713696...

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

%t t = x /. FindRoot[E^(-x) == Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t] (* Cf. A069997 *)

%t t = x /. FindRoot[E^(-x) == 2 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196407 *)

%t t = x /. FindRoot[E^(-x) == 3 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196408 *)

%t t = x /. FindRoot[E^(-x) == 4 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196409 *)

%t t = x /. FindRoot[E^(-x) == 5 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196462 *)

%t t = x /. FindRoot[E^(-x) == 6 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196463 *)

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 02 2011