

A194745


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


3



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
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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



