A123724 - OEIS

A123724

Partial sums of (-1)^floor(n*2^(1/3)).

-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

(list; graph; refs; listen; history; text; internal format)

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

T. D. Noe, Table of n, a(n) for n=1..40000

T. D. Noe, Plot of 10^6 terms

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]]]]