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

1,5

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. A194745, A194738.

Sequence in context: A261218 A094097 A145330 * A132669 A276052 A348340

Adjacent sequences: A194741 A194742 A194743 * A194745 A194746 A194747

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved