A194749 Number of k such that {-k*sqrt(6)} > {-n*sqrt(6)}, where { } = fractional part.

0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 10, 4, 10, 3, 10, 2, 10, 1, 10, 19, 8, 18, 6, 17, 4, 16, 2, 15, 0, 14, 28, 11, 26, 8, 24, 5, 22, 2, 20, 38, 16, 35, 12, 32, 8, 29, 4, 26, 0, 23, 46, 18, 42, 13, 38, 8, 34, 3, 30, 57, 24, 52, 18, 47, 12, 42, 6, 37, 0, 32, 64, 25, 58, 18, 52, 11

Offset

1,4

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}]   (* A194748 *)
Table[t[n], {n, 1, 100}]   (* A194749 *)

Crossrefs

Cf. A194748, A194738.

Sequence in context: A008802 A008809 A008821 * A284969 A097852 A008801

Adjacent sequences: A194746 A194747 A194748 * A194750 A194751 A194752

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved