A123738 Partial sums of (-1)^floor(n*Pi).

-1, 0, -1, 0, -1, 0, -1, -2, -1, -2, -1, -2, -1, -2, -3, -2, -3, -2, -3, -2, -3, -4, -3, -4, -3, -4, -3, -4, -5, -4, -5, -4, -5, -4, -5, -6, -5, -6, -5, -6, -5, -6, -7, -6, -7, -6, -7, -6, -7, -8, -7, -8, -7, -8, -7, -8, -9, -8, -9, -8, -9, -8, -9, -10, -9, -10, -9, -10, -9, -10, -11, -10, -11, -10, -11, -10, -11, -12, -11, -12

Offset

1,8

Links

T. D. Noe, Table of n, a(n) for n=1..10000

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[Pi*Range[120]]]]

Prog

(PARI) vector(130, n, sum(j=1, n, (-1)^(j\(1/Pi))) ) \\ G. C. Greubel, Sep 05 2019
(Magma) R:= RealField(20); [&+[(-1)^Floor(j*Pi(R)): j in [1..n]]: n in [1..130]]; // G. C. Greubel, Sep 05 2019
(Sage) [sum((-1)^floor(j*pi) for j in (1..n)) for n in (1..130)] # G. C. Greubel, Sep 05 2019

Crossrefs

Cf. A123724 (sum for 2^(1/3)), A123737 (sum for sqrt(2)), A123739 (sum for e).

Sequence in context: A275344 A206826 A175835 * A194511 A214526 A245038

Adjacent sequences: A123735 A123736 A123737 * A123739 A123740 A123741

Keyword

easy,sign

Author

T. D. Noe, Oct 11 2006

Status

approved