%I #21 Nov 14 2019 11:21:36
%S 0,6,12,56,100,144,188,521,1231,1941,2651,3361,4071,4781,5491,6201,
%T 6911,7621,8331,9041,9751,10461,11171,11881,12591,13301,14011,14721,
%U 15431,16141,16851,17561,18271,18981,19691,20401,21111,21821,22531,23241,23951,24661,25371,26081,26791,27501,28211,28921,29631
%N Indices n for which the partial sums of sin(k) (0 <= k <= n) reach a new minimum.
%e The partial sums are 0, 0.84147.. = A049469, 1.7507.., 1.89188.., 1.13508.., 0.1761..., -0.1032..., 0.5537,..., and -0.1032.. is the first to become smaller than 0, so a(1)=6. - _R. J. Mathar_, Nov 14 2019
%t n = 30000;
%t i = Range[0, n];
%t x = Accumulate[N[Sin[i]]];
%t y = Table[Min[x[[1 ;; k]]], {k, n + 1}];
%t z = DeleteDuplicatesBy[Transpose[{i, y}], Last][[All, 1]]
%o (Python)
%o x = numpy.arange(n)
%o y = numpy.sin(x)
%o y = numpy.cumsum(y)
%o y = numpy.minimum.accumulate(y)
%o y = numpy.diff(y)
%o y = numpy.insert(y, 0, -1)
%o x[y < 0.]
%K nonn
%O 0,2
%A _Josselin Noirel_, Dec 04 2018