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

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]]]]
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

Adjacent sequences: A123721 A123722 A123723 * A123725 A123726 A123727

Keyword

easy,nice,sign,look

Author

T. D. Noe, Oct 11 2006

Status

approved