

A194734


Number of k such that {k*r} > {n*r}, where { } = fractional part, r = (1+sqrt(5))/2 (the golden ratio).


2



0, 0, 2, 1, 0, 4, 2, 7, 4, 1, 8, 4, 0, 9, 4, 14, 8, 2, 14, 7, 20, 12, 4, 19, 10, 1, 18, 8, 26, 15, 4, 24, 12, 0, 22, 9, 32, 18, 4, 29, 14, 40, 24, 8, 36, 19, 2, 32, 14, 45, 26, 7, 40, 20, 54, 33, 12, 48, 26, 4, 42, 19, 58, 34, 10, 51, 26, 1, 44, 18, 62, 35, 8, 54, 26, 73, 44
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..77.


MATHEMATICA

r = GoldenRatio; 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}] (* A019588 *)
Table[t[n], {n, 1, 100}] (* A193734 *)


CROSSREFS

Cf. A019588, A194738.
Sequence in context: A002349 A096794 A106375 * A255528 A201701 A131667
Adjacent sequences: A194731 A194732 A194733 * A194735 A194736 A194737


KEYWORD

nonn


AUTHOR

Clark Kimberling, Sep 02 2011


STATUS

approved



