Products of Farey Fractions
نویسندگان
چکیده
منابع مشابه
The Correlations of Farey Fractions
We prove that all correlations of the sequence of Farey fractions exist and provide formulas for the correlation measures.
متن کاملOn the Index of Farey Sequences
For any two consecutive Farey fractions γi = ai/qi < γi+1 = ai+1/qi+1, one has ai+1qi − aiqi+1 = 1 and qi + qi+1 > Q. Conversely, if q and q ′ are two coprime integers in {1, . . . , Q} with q + q > Q, then there are unique a ∈ {1, . . . , q} and a ∈ {1, . . . , q} for which aq − aq = 1, and a/q < a/q are consecutive Farey fractions of order Q. Therefore, the pairs of coprime integers (q, q) wi...
متن کاملA Farey Sequence of Fibonacci Numbers
The Farey sequence is an old and famous set of fractions associated with the integers. We here show that if we form a Farey sequence of Fibonacci Numbers, the properties of the Farey sequence are remarkably preserved (see [2]). In fact we find that with the new sequence we are able to observe and identify "points of symmetry/' "intervals," "generating fractions" and "stages." The paper is divid...
متن کاملThe Distribution of Special Subsets of the Farey Sequence
We will examine the subset FQ,p of Farey fractions of order Q consisting of those fractions whose denominators are not divisible by a fixed prime p. In particular, we will provide an asymptotic result on the distribution of H−tuples of consecutive fractions in FQ,p, as Q → ∞.
متن کاملNumerators of Differences of Nonconsecutive Farey Fractions
Abstract. An elementary but useful fact is that the numerator of the difference of two consecutive Farey fractions is equal to one. For triples of consecutive fractions the numerators of the differences are well understood and have applications to several interesting problems. In this paper we investigate numerators of differences of fractions which are farther apart. We establish algebraic ide...
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عنوان ژورنال:
- Experimental Mathematics
دوره 26 شماره
صفحات -
تاریخ انتشار 2017