

A194814


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).


2



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

1,2


COMMENTS

A194813+A194814=A000027 for n>0.


LINKS

Table of n, a(n) for n=1..72.


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. A194813, A194738.
Sequence in context: A157477 A248801 A006949 * A055748 A284520 A342248
Adjacent sequences: A194811 A194812 A194813 * A194815 A194816 A194817


KEYWORD

nonn


AUTHOR

Clark Kimberling, Sep 03 2011


STATUS

approved



