A196407 Decimal expansion of the least positive number x satisfying e^(-x)=2*sin(x).

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, 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, 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

Offset

0,1

Links

Table of n, a(n) for n=0..99.

Example

x=0.3573274113225554808314246748121123097128278224830566...

Mathematica

Plot[{E^(-x), Sin[x], 2 Sin[x], 3 Sin[x], 4 Sin[x]}, {x, 0, Pi/2}]
t = x /. FindRoot[E^(-x) == Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* Cf. A069997 *)
t = x /. FindRoot[E^(-x) == 2 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196407 *)
t = x /. FindRoot[E^(-x) == 3 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196408 *)
t = x /. FindRoot[E^(-x) == 4 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196409 *)
t = x /. FindRoot[E^(-x) == 5 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196462 *)
t = x /. FindRoot[E^(-x) == 6 Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196463 *)

Crossrefs

Cf. A196396, A196401.

Sequence in context: A367289 A351463 A121573 * A156030 A338974 A255562

Adjacent sequences: A196404 A196405 A196406 * A196408 A196409 A196410

Keyword

nonn,cons

Author

Clark Kimberling, Oct 02 2011

Status

approved