A194747 Number of k such that {k*sqrt(6)} > {n*sqrt(6)}, where { } = fractional part.

0, 0, 2, 1, 4, 2, 6, 3, 8, 4, 0, 7, 2, 10, 4, 13, 6, 16, 8, 0, 12, 3, 16, 6, 20, 9, 24, 12, 28, 15, 2, 20, 6, 25, 10, 30, 14, 35, 18, 1, 24, 6, 30, 11, 36, 16, 42, 21, 48, 26, 4, 33, 10, 40, 16, 47, 22, 54, 28, 2, 36, 9, 44, 16, 52, 23, 60, 30, 68, 37, 6, 46, 14, 55, 22, 64

Offset

1,3

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. A194746, A194738.

Sequence in context: A130742 A130107 A107130 * A065423 A239242 A340621

Adjacent sequences: A194744 A194745 A194746 * A194748 A194749 A194750

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved