A194744 Number of k such that {-k*sqrt(5)} < {-n*sqrt(5)}, where { } = fractional part.

1, 1, 1, 1, 5, 4, 3, 2, 9, 7, 5, 3, 13, 10, 7, 4, 17, 13, 9, 5, 1, 18, 13, 8, 3, 23, 17, 11, 5, 28, 21, 14, 7, 33, 25, 17, 9, 1, 31, 22, 13, 4, 37, 27, 17, 7, 43, 32, 21, 10, 49, 37, 25, 13, 1, 44, 31, 18, 5, 51, 37, 23, 9, 58, 43, 28, 13, 65, 49, 33, 17, 1, 57, 40, 23, 6

Offset: 1

Author

Clark Kimberling, Sep 02 2011

Keywords

• nonn

Crossrefs

Cf. A194745, A194738.

Programs

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 *)