Experimental Mathematics

Spot-Based Generations for Meta-Fibonacci Sequences

Barnaby Dalton, Mustazee Rahman, and Stephen Tanny

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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.

Article information

Experiment. Math., Volume 20, Issue 2 (2011), 129-137.

First available in Project Euclid: 6 October 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11B37: Recurrences {For applications to special functions, see 33-XX}
Secondary: 39A99: None of the above, but in this section

Connolly sequence Conway sequence meta-Fibonacci sequence spot-based generation spot function


Dalton, Barnaby; Rahman, Mustazee; Tanny, Stephen. Spot-Based Generations for Meta-Fibonacci Sequences. Experiment. Math. 20 (2011), no. 2, 129--137. https://projecteuclid.org/euclid.em/1317924404

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