Spot-Based Generations for Meta-Fibonacci Sequences

Details Spot-Based Generations for Meta-Fibonacci Sequences Spot-Based Generations for Meta-Fibonacci Sequences

2011-05-09

arxiv.org/abs/1105.1797v1

Experimental Mathematics, 20 (2): 129-137, 2011

Mathematics

Combinatorics

11 pages, 4 figures

Scientific paper

10.1080/10586458.2011.544565

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.

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