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A VARIANT OF HOFSTADTER’S SEQUENCE AND FINITE AUTOMATA

Part of: Sequences and sets Elementary number theory

Published online by Cambridge University Press:  03 May 2013

JEAN-PAUL ALLOUCHE  and
JEFFREY SHALLIT
JEAN-PAUL ALLOUCHE
Affiliation:
CNRS, Institut de Mathématiques, Université Pierre et Marie Curie, Case 247, 4 place Jussieu, F-75752 Paris Cedex 05, France email [email protected]
JEFFREY SHALLIT*
Affiliation:
School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
*
✉[email protected]
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Abstract

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Following up on a paper of Balamohan et al. [‘On the behavior of a variant of Hofstadter’s $q$-sequence’, J. Integer Seq. 10 (2007)], we analyze a variant of Hofstadter’s $Q$-sequence and show that its frequency sequence is 2-automatic. An automaton computing the sequence is explicitly given.

Keywords

Hofstadter’s sequencerecurrenceautomatic sequencefinite automaton

MSC classification

Secondary: 11B85: Automata sequences 11B37: Recurrences 11B39: Fibonacci and Lucas numbers and polynomials and generalizations 11A63: Radix representation; digital problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 93 , Issue 1-2 , October 2012 , pp. 1 - 8
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc.

References

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