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%I #11 Oct 03 2017 05:42:49
%S -1,0,-1,-2,-1,-2,-1,0,-1,0,-1,-2,-1,-2,-1,0,-1,0,-1,-2,-1,-2,-1,0,-1,
%T 0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,2,1,2,
%U 1,0,1,0,1,2,1,2,1,0,1,0,1,2,1,2,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,1,0,1,0
%N Partial sums of (-1)^floor(n*2^(1/3)).
%C Remarkably, these partial sums appear to have several periods of length 153008. This sum is not discussed by O'Bryant et al.
%H T. D. Noe, <a href="/A123724/b123724.txt">Table of n, a(n) for n=1..40000</a>
%H T. D. Noe, <a href="http://www.sspectra.com/math/A123724.png">Plot of 10^6 terms</a>
%H Kevin O'Bryant, Bruce Reznick and Monika Serbinowska, <a href="https://arxiv.org/abs/math/0308087">Almost alternating sums</a>, arXiv:math/0308087 [math.NT], 2003-2005.
%H Kevin O'Bryant, Bruce Reznick and Monika Serbinowska, <a href="http://www.jstor.org/stable/27642030">Almost alternating sums</a>, Amer. Math. Monthly, Vol. 113 (October 2006), 673-688.
%t Rest[FoldList[Plus,0,(-1)^Floor[2^(1/3)*Range[120]]]]
%t Accumulate[(-1)^Floor[Range[100]Surd[2,3]]] (* _Harvey P. Dale_, Apr 16 2015 *)
%Y Cf. A123737 (sum for sqrt(2)), A123738 (sum for Pi), A123739 (sum for e).
%K easy,nice,sign,look
%O 1,4
%A _T. D. Noe_, Oct 11 2006
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