×

zbMATH — the first resource for mathematics

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.
MSC:
11Y55 Calculation of integer sequences
11A25 Arithmetic functions; related numbers; inversion formulas
11B83 Special sequences and polynomials
PDF BibTeX XML Cite
Full Text: EMIS EuDML