A194740 Number of k such that {-k*sqrt(3)} < {-n*sqrt(3)}, where { } = fractional part.

1, 2, 3, 1, 3, 5, 7, 2, 5, 8, 11, 3, 7, 11, 1, 6, 11, 16, 3, 9, 15, 21, 5, 12, 19, 26, 7, 15, 23, 2, 11, 20, 29, 5, 15, 25, 35, 8, 19, 30, 41, 11, 23, 35, 3, 16, 29, 42, 7, 21, 35, 49, 11, 26, 41, 1, 17, 33, 49, 6, 23, 40, 57, 11, 29, 47, 65, 16, 35, 54, 3, 23, 43, 63, 9

Offset

1,2

Links

Table of n, a(n) for n=1..75.

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. A194741, A194738.

Sequence in context: A255437 A162609 A194752 * A194762 A054250 A193923

Adjacent sequences: A194737 A194738 A194739 * A194741 A194742 A194743

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved