Journal of Integer Sequences, Vol. 9 (2006), Article 06.3.4 |

Institute of Mathematics of the Romanian Academy

P. O. Box 1-764

Bucharest 70700

Romania

**Abstract:**

Let
be the set of Farey fractions of order .
Given the integers
and
, let
be
the subset of
of those fractions whose denominators are
(mod
, arranged in ascending order. The problem we
address here is to show that as
,
there exists a limit probability measuring the distribution of -tuples
of consecutive denominators of fractions in
.
This shows that the clusters of points
, where
are consecutive denominators of members of
produce a limit set,
denoted by
.
The shape and the structure of this set are presented in several
particular cases.

Received September 15 2004;
revised version received May 20 2005; July 20 2006.
Published in *Journal of Integer Sequences* July 20 2006.

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