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

Author

T. D. Noe, Oct 11 2006

Keywords

• easy
• sign

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.

Crossrefs

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

Programs

Magma

R:= RealField(20); [&+[(-1)^Floor(j*Pi(R)): j in [1..n]]: n in [1..130]]; // G. C. Greubel, Sep 05 2019

Mathematica

Rest[FoldList[Plus,0,(-1)^Floor[Pi*Range[120]]]]

PARI

vector(130, n, sum(j=1,n, (-1)^(j\(1/Pi))) ) \\ 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