%I #7 Aug 09 2021 13:59:59

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

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

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

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

%e x=0.259948213533212806677522636846326798938719239635636...

%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