A194741 Number of k such that {-k*sqrt(3)} > {-n*sqrt(3)}, where { } = fractional part.

0, 0, 0, 3, 2, 1, 0, 6, 4, 2, 0, 9, 6, 3, 14, 10, 6, 2, 16, 11, 6, 1, 18, 12, 6, 0, 20, 13, 6, 28, 20, 12, 4, 29, 20, 11, 2, 30, 20, 10, 0, 31, 20, 9, 42, 30, 18, 6, 42, 29, 16, 3, 42, 28, 14, 55, 40, 25, 10, 54, 38, 22, 6, 53, 36, 19, 2, 52, 34, 16, 68, 49, 30, 11, 66, 46

Offset

1,4

Links

Table of n, a(n) for n=1..76.

Mathematica

Remove["Global`*"];
r = -Sqrt[3]; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
s[n_] := Sum[u[n, k], {k, 1, n}]
t[n_] := Sum[v[n, k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194740 *)
Table[t[n], {n, 1, 100}]   (* A194741 *)

Crossrefs

Cf. A194740, A194738.

Sequence in context: A084269 A051427 A194763 * A194753 A359400 A373072

Adjacent sequences: A194738 A194739 A194740 * A194742 A194743 A194744

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved