%I #7 Feb 22 2025 20:29:23
%S 3,5,7,3,2,7,4,1,1,3,2,2,5,5,5,4,8,0,8,3,1,4,2,4,6,7,4,8,1,2,1,1,2,3,
%T 0,9,7,1,2,8,2,7,8,2,2,4,8,3,0,5,6,6,1,0,1,8,3,6,4,3,0,8,6,0,7,7,5,4,
%U 3,8,0,5,1,4,6,5,6,3,9,8,4,0,4,3,7,5,8,8,0,5,0,8,3,9,1,8,4,7,9,1
%N Decimal expansion of the least positive number x satisfying e^(-x)=2*sin(x).
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e 0.3573274113225554808314246748121123097128278224830566...
%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 *)
%Y Cf. A196396, A196401.
%K nonn,cons,changed
%O 0,1
%A _Clark Kimberling_, Oct 02 2011