A194824 a(n) = 2+floor(sum{<((-1)^k)*k*sqrt(3)> : 1<=k<=n}), where < > = fractional part.

1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 2, 3, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3

Offset

1,4

Comments

The first negative term is a(5431) = -1. - Georg Fischer, Feb 15 2019

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Mathematica

r = Sqrt[3]; p[x_] := FractionalPart[x];
f[n_] := 2 + Floor[Sum[p[k*r] (-1)^k, {k, 1, n}]]
Table[f[n], {n, 1, 1000}]   (* A194824 *)

Prog

(PARI) for(n=1, 50, print1(2 + floor(sum(k=1, n, (-1)^k*frac(k*sqrt(3))), ", ")) \\ G. C. Greubel, Apr 02 2018
(Magma) [2 + Floor((&+[(-1)^k*(k*Sqrt(3) - Floor(k*Sqrt(3))) :k in [1..n]])) : n in [1..50]]; // G. C. Greubel, Apr 02 2018

Crossrefs

Cf. A194821, A194822, A194823.

Sequence in context: A283876 A365663 A067754 * A339931 A339221 A025851

Adjacent sequences: A194821 A194822 A194823 * A194825 A194826 A194827

Keyword

sign

Author

Clark Kimberling, Sep 03 2011

Status

approved