Spot-Based Generations for Meta-Fibonacci Sequences
| Autor: | Stephen M. Tanny, Barnaby Dalton, Mustazee Rahman |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Large class
meta-Fibonacci sequence Fibonacci number Mathematics - Number Theory 39A99 General Mathematics spot-based generation Chaotic 11B37 Connolly sequence spot function Conway sequence Combinatorics 11B37 (Primary) 39A99 (Secondary) FOS: Mathematics Partition (number theory) Mathematics - Combinatorics Combinatorics (math.CO) Number Theory (math.NT) Mathematics |
| Zdroj: | Experiment. Math. 20, iss. 2 (2011), 129-137 |
| DOI: | 10.48550/arxiv.1105.1797 |
| Popis: | For many meta-Fibonacci sequences it is possible to identify a partition of the sequence into successive intervals (sometimes called blocks) with the property that the sequence behaves "similarly" in each block. This partition provides insights into the sequence properties. To date, for any given sequence, only ad hoc methods have been available to identify this partition. We apply a new concept - the spot-based generation sequence - to derive a general methodology for identifying this partition for a large class of meta-Fibonacci sequences. This class includes the Conolly and Conway sequences and many of their well-behaved variants, and even some highly chaotic sequences, such as Hofstadter's famous Q-sequence. Comment: 11 pages, 4 figures |
| Databáze: | OpenAIRE |
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