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A123724
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Partial sums of (-1)^floor(n*2^(1/3)).
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4
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-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
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OFFSET
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1,4
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COMMENTS
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Remarkably, these partial sums appear to have several periods of length 153008. This sum is not discussed by O'Bryant et al.
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LINKS
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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