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A123724
Partial sums of (-1)^floor(n*2^(1/3)).
4
-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, 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, 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
OFFSET
1,4
COMMENTS
Remarkably, these partial sums appear to have several periods of length 153008. This sum is not discussed by O'Bryant et al.
LINKS
Kevin O'Bryant, Bruce Reznick and Monika Serbinowska, Almost alternating sums, arXiv:math/0308087 [math.NT], 2003-2005.
Kevin O'Bryant, Bruce Reznick and Monika Serbinowska, Almost alternating sums, Amer. Math. Monthly, Vol. 113 (October 2006), 673-688.
MATHEMATICA
Rest[FoldList[Plus, 0, (-1)^Floor[2^(1/3)*Range[120]]]]
Accumulate[(-1)^Floor[Range[100]Surd[2, 3]]] (* Harvey P. Dale, Apr 16 2015 *)
CROSSREFS
Cf. A123737 (sum for sqrt(2)), A123738 (sum for Pi), A123739 (sum for e).
Sequence in context: A228109 A318682 A339455 * A107016 A318702 A360536
KEYWORD
easy,nice,sign,look
AUTHOR
T. D. Noe, Oct 11 2006
STATUS
approved