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%I #11 Apr 11 2024 14:59:05
%S 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,
%T 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,
%U 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
%N Decimal expansion of the infinite sum Sum_{k>=1} sin(k)/k!.
%C 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
%F From _Amiram Eldar_, Jul 19 2020: (Start)
%F Equals e^cos(1) * sin(sin(1)).
%F Equals sin(sin(1)) * (cosh(cos(1)) + sinh(cos(1))).
%F Equals (-i)*(e^(e^i) - e^(e^(-i)))/2. (End)
%e 1.279883001373022493908...
%t Sum[N[Sin[i], 400]/i!, {i, 1, 300}] (which is accurate to 300 digits).
%o (PARI) suminf(k=1, sin(k)/k!) \\ _Michel Marcus_, Jul 19 2020
%Y Cf. A001113, A049469, A049470, A114941.
%K nonn,cons,changed
%O 1,2
%A _Stefan Steinerberger_, Feb 21 2006
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