A194745 Number of k such that {-k*sqrt(5)} > {-n*sqrt(5)}, where { } = fractional part.

0, 1, 2, 3, 0, 2, 4, 6, 0, 3, 6, 9, 0, 4, 8, 12, 0, 5, 10, 15, 20, 4, 10, 16, 22, 3, 10, 17, 24, 2, 10, 18, 26, 1, 10, 19, 28, 37, 8, 18, 28, 38, 6, 17, 28, 39, 4, 16, 28, 40, 2, 15, 28, 41, 54, 12, 26, 40, 54, 9, 24, 39, 54, 6, 22, 38, 54, 3, 20, 37, 54, 71, 16, 34, 52, 70

Offset

1,3

Links

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

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}]   (* A194744 *)
Table[t[n], {n, 1, 100}]   (* A194745 *)

Crossrefs

Cf. A194744, A194738.

Sequence in context: A328568 A219864 A257844 * A248342 A002392 A002708

Adjacent sequences: A194742 A194743 A194744 * A194746 A194747 A194748

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved