%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