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

Author

T. D. Noe, Oct 11 2006

Keywords

• easy
• nice
• sign
• look

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.

Crossrefs

Cf. A123737 (sum for sqrt(2)), A123738 (sum for Pi), A123739 (sum for e).

Programs

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 *)