A114940 Decimal expansion of the infinite sum Sum_{k>=1} sin(k)/k!.

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

Offset

1,2

Comments

This is the imaginary part of exp(exp(i)), i the imaginary unit, where the real part is 1+A114941. - R. J. Mathar, Apr 11 2024

Links

Table of n, a(n) for n=1..106.

Formula

From Amiram Eldar, Jul 19 2020: (Start)

Equals e^cos(1) * sin(sin(1)).

Equals sin(sin(1)) * (cosh(cos(1)) + sinh(cos(1))).

Equals (-i)*(e^(e^i) - e^(e^(-i)))/2. (End)

Example

1.279883001373022493908...

Mathematica

Sum[N[Sin[i], 400]/i!, {i, 1, 300}] (which is accurate to 300 digits).

Prog

(PARI) suminf(k=1, sin(k)/k!) \\ Michel Marcus, Jul 19 2020

Crossrefs

Cf. A001113, A049469, A049470, A114941.

Sequence in context: A339237 A363078 A377479 * A120483 A124823 A086725

Adjacent sequences: A114937 A114938 A114939 * A114941 A114942 A114943

Keyword

nonn,cons

Author

Stefan Steinerberger, Feb 21 2006

Status

approved