A194739 Number of k such that {k*sqrt(3)} > {n*sqrt(3)}, where { } = fractional part.

0, 1, 2, 0, 2, 4, 6, 1, 4, 7, 10, 2, 6, 10, 0, 5, 10, 15, 2, 8, 14, 20, 4, 11, 18, 25, 6, 14, 22, 1, 10, 19, 28, 4, 14, 24, 34, 7, 18, 29, 40, 10, 22, 34, 2, 15, 28, 41, 6, 20, 34, 48, 10, 25, 40, 0, 16, 32, 48, 5, 22, 39, 56, 10, 28, 46, 64, 15, 34, 53, 2, 22, 42, 62, 8

Offset

1,3

Links

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

Mathematica

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}]   (* A194738 *)
Table[t[n], {n, 1, 100}]   (* A194739 *)

Crossrefs

Cf. A194738.

Sequence in context: A077484 A182064 A194751 * A194765 A239229 A058210

Adjacent sequences: A194736 A194737 A194738 * A194740 A194741 A194742

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved