A194746 Number of k such that {k*sqrt(6)} < {n*sqrt(6)}, where { } = fractional part.

1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 11, 5, 11, 4, 11, 3, 11, 2, 11, 20, 9, 19, 7, 18, 5, 17, 3, 16, 1, 15, 29, 12, 27, 9, 25, 6, 23, 3, 21, 39, 17, 36, 13, 33, 9, 30, 5, 27, 1, 24, 47, 19, 43, 14, 39, 9, 35, 4, 31, 58, 25, 53, 19, 48, 13, 43, 7, 38, 1, 33, 65, 26, 59, 19, 53, 12

Offset

1,2

Links

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

Mathematica

r = Sqrt[6]; 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}]   (* A194746 *)
Table[t[n], {n, 1, 100}]   (* A194747 *)

Crossrefs

Cf. A194747, A194738.

Sequence in context: A229994 A165818 A369895 * A198336 A365431 A353960

Adjacent sequences: A194743 A194744 A194745 * A194747 A194748 A194749

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved