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%I #14 Sep 19 2017 12:07:05
%S 1,0,1,3,9,5,9,1,3,2,3,6,0,7,6,8,5,0,4,2,9,4,5,7,4,3,3,8,8,8,5,9,1,4,
%T 6,8,7,5,6,1,1,7,9,2,8,0,0,7,7,7,1,7,3,1,6,8,7,7,0,4,8,5,1,2,2,6,8,1,
%U 3,7,8,1,2,3,4,6,0,7,9,5,5,7,3,3,6,3,8,8,2,1,8,6,5,4,7,7,1,2,2,0,4,2,1,5,7
%N Decimal expansion of Sum_{k >= 1} sin(k)/k^2.
%C Also, decimal expansion of the imaginary part of Sum_{k>=1} e^(i*k)/k^2. [_Bruno Berselli_, Mar 24 2013]
%H I. Rosenholtz, <a href="http://www.jstor.org/stable/2690793">Tangent sequences, world records, ...</a>, Math. Mag., 72 (No. 5, 1999), 367-376.
%e 1.013959132360768504294574338885914687561179280077717316877048512268137...
%t $MaxExtraPrecision = 128; RealDigits[ Chop[ N[ I/2*(PolyLog[2, E^-I] - PolyLog[2, E^I]), 105]]][[1]] (* _Robert G. Wilson v_, Aug 16 2004 *)
%o (PARI) imag(polylog(2,exp(I))) \\ _Charles R Greathouse IV_, Jul 14 2014
%Y Cf. A096444, A096464.
%Y Cf. A122143 (decimal expansion of Sum_{k >= 1} cos(k)/k^2).
%K nonn,cons
%O 1,4
%A _N. J. A. Sloane_, Aug 16 2004
%E More terms from _Robert G. Wilson v_, Aug 17 2004
%E Sequence checked by _T. D. Noe_, Aug 21 2006
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