

A194743


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


3



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
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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: A194764 A194738 A194750 * A113778 A295673 A155172
Adjacent sequences: A194740 A194741 A194742 * A194744 A194745 A194746


KEYWORD

nonn


AUTHOR

Clark Kimberling, Sep 02 2011


STATUS

approved



