A123739 Partial sums of (-1)^floor(n*e).

1, 0, 1, 2, 1, 2, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 2, 1, 2, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1

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, Amer. Math. Monthly, Vol. 113 (October 2006), 673-688.

Crossrefs

Cf. A123724 (sum for 2^(1/3)), A123737 (sum for sqrt(2)), A123738 (sum for pi).

Programs

Magma

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

Mathematica

Rest[FoldList[Plus,0,(-1)^Floor[E*Range[120]]]]
Accumulate[(-1)^Floor[E Range[200]]] (* Harvey P. Dale, May 06 2022 *)

PARI

vector(50, n, sum(j=1,n, (-1)^(j\exp(-1))) ) \\ G. C. Greubel, Sep 05 2019

Sage

[sum((-1)^floor(j*exp(1)) for j in (1..n)) for n in (1..130)] # G. C. Greubel, Sep 05 2019