## Abstract

Let F-fraktur sign^{Q} be the set of Farey fractions of order Q. Given the integers ∂ ≥ 2 and 0 ≤ c ≤ ∂ -1, let F-fraktur sign^{Q}(c, ∂) be the subset of F-fraktur sign^{Q} of those fractions whose denominators are = c (mod ∂), arranged in ascending order. The problem we address here is to show that as Q → ∞, there exists a limit probability measuring the distribution of s-tuples of consecutive denominators of fractions in F-fraktur sign^{Q}(c, ∂). This shows that the clusters of points (q_{0}/Q, q_{1}/Q,....,q _{s}/Q) [0, 1]^{s+1}, where q_{0}, q_{1},..., q_{s} are consecutive denominators of members of F-fraktur sign ^{Q} produce a limit set, denoted by D(c, ∂). The shape and the structure of this set are presented in several particular cases.

Original language | English (US) |
---|---|

Pages (from-to) | 1-26 |

Number of pages | 26 |

Journal | Journal of Integer Sequences |

Volume | 9 |

Issue number | 3 |

State | Published - Jul 20 2006 |

## Keywords

- Arithmetic progressions
- Congruence constraints
- Farey fractions

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics