

A194813


Number of integers k in [1,n] such that {n*r+k*r} < {n*rk*r}, where { } = fractional part and r=(1+sqrt(5))/2 (the golden ratio).


7



0, 0, 1, 2, 2, 2, 3, 4, 5, 5, 5, 6, 6, 6, 6, 7, 8, 8, 8, 9, 10, 11, 11, 12, 13, 13, 13, 13, 14, 15, 15, 15, 16, 16, 16, 16, 17, 18, 18, 18, 19, 20, 21, 21, 22, 23, 23, 23, 23, 24, 25, 25, 25, 26, 27, 28, 28, 29, 30, 30, 30, 31, 32, 33, 33, 33, 34, 34, 34, 34, 35, 36, 36
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OFFSET

1,4


COMMENTS

A194813+A194814=A000027 for n>0.


LINKS

Table of n, a(n) for n=1..73.


EXAMPLE

{4r+1r}=0.09...; {4r1r}=0.85...;
{4r+2r}=0.70...; {4r2r}=0.23...;
{4r+3r}=0.32...; {4r3r}=0.61...;
{4r+4r}=0.94...; {4r4r}=0.00...;
so that a(4)=2.


MATHEMATICA

r = GoldenRatio; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[n*r + k*r] <= p[n*r  k*r], 1, 0]
v[n_, k_] := If[p[n*r + k*r] > p[n*r  k*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}] (* A194813 *)
Table[t[n], {n, 1, 100}] (* A194814 *)


CROSSREFS

Cf. A194814, A194738.
Sequence in context: A266686 A162352 A285509 * A096533 A230413 A029096
Adjacent sequences: A194810 A194811 A194812 * A194814 A194815 A194816


KEYWORD

nonn


AUTHOR

Clark Kimberling, Sep 03 2011


STATUS

approved



