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Further results on derived sequences. (English) Zbl 1058.11080
C. L. Cohen and D. E. Iannucci [J. Integer Seq., 6, No. 1, Art. 03.1.1 (2003; Zbl 1014.11069)] introduced the derived sequence of a positive integer \(n\) and showed they are bounded for all \(n< 1.5\times 10^{10}\). Bounded sequences end in a cycle, and they conjectured the existence of cycles of any order. This paper proves this conjecture and shows how to construct derived sequences of any order.
11Y55 Calculation of integer sequences
11A25 Arithmetic functions; related numbers; inversion formulas
11B83 Special sequences and polynomials
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