A194743 Number of k such that {k*sqrt(5)} > {n*sqrt(5)}, where { } = fractional part.

0, 0, 0, 0, 4, 3, 2, 1, 8, 6, 4, 2, 12, 9, 6, 3, 16, 12, 8, 4, 0, 17, 12, 7, 2, 22, 16, 10, 4, 27, 20, 13, 6, 32, 24, 16, 8, 0, 30, 21, 12, 3, 36, 26, 16, 6, 42, 31, 20, 9, 48, 36, 24, 12, 0, 43, 30, 17, 4, 50, 36, 22, 8, 57, 42, 27, 12, 64, 48, 32, 16, 0, 56, 39, 22, 5, 64

Offset

1,5

Links

Table of n, a(n) for n=1..77.

Mathematica

r = Sqrt[5]; 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}]   (* A194742 *)
Table[t[n], {n, 1, 100}]   (* A194743 *)

Crossrefs

Cf. A194743, A194738.

Sequence in context: A194738 A194750 A370350 * A113778 A295673 A155172

Adjacent sequences: A194740 A194741 A194742 * A194744 A194745 A194746

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved