Cycles of higher-order Collatz sequences
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Published:2022-02
Issue:1
Volume:28
Page:48-63
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ISSN:1310-5132
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Container-title:Notes on Number Theory and Discrete Mathematics
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language:
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Short-container-title:NNTDM
Abstract
Consider a sequence of numbers x_n \in \mathbb{Z_+} defined by x_{n+1}= \frac{x_n}{2} if x_n is even, and x_{n+1}= \frac{x_n+2x_{n-1}+q}{2} if x_n is odd. A 1-cycle is a periodic sequence with one transition from odd to even numbers. We prove theoretical and computational results for the existence of 1-cycles, and discuss a generalization to more complex cycles.
Publisher
Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences)