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2011 Spot-Based Generations for Meta-Fibonacci Sequences
Barnaby Dalton, Mustazee Rahman, Stephen Tanny
Experiment. Math. 20(2): 129-137 (2011).

Abstract

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.

Citation

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Barnaby Dalton. Mustazee Rahman. Stephen Tanny. "Spot-Based Generations for Meta-Fibonacci Sequences." Experiment. Math. 20 (2) 129 - 137, 2011.

Information

Published: 2011
First available in Project Euclid: 6 October 2011

zbMATH: 1269.11013
MathSciNet: MR2821384

Subjects:
Primary: 11B37
Secondary: 39A99

Keywords: Connolly sequence , Conway sequence , meta-Fibonacci sequence , spot function , spot-based generation

Rights: Copyright © 2011 A K Peters, Ltd.

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Vol.20 • No. 2 • 2011
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