Investigates maximum gaps between fractions in Farey sequences, indicating important numerical patterns.
Let D ≥ 2 be an integer, and let ΦQ be a classical Farey sequence of order Q . Let us mark the fractions of this sequence whose denominators belong to a given arithmetic progression with difference D . What is the maximum number of fractions in the interval between two adjacent marked fractions? In this paper, we obtain precise formulas for these quantities in the case of $$D=3$$ .
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K. S. Arzhanykh (2025) studied this question.
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