A194739 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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 *)