Conway's Subprime Fibonacci Sequences

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Dec 2014Embargo end date: 01 Jan 2012 English Publisher:Informa UK LimitedJournal:Mathematics Magazine, volume 87, pages 323-337 (issn: 0025-570X, eissn: 1930-0980,

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Authors: Guy, Richard K.; Khovanova, Tanya; Salazar, Julian;

doi: 10.4169/math.mag.87.5.323 , 10.48550/arxiv.1207.5099

arXiv: 1207.5099

Conway's Subprime Fibonacci Sequences

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Abstract

It's the age-old recurrence with a twist: sum the last two terms and if the result is composite, divide by its smallest prime divisor to get the next term (e.g., 0, 1, 1, 2, 3, 5, 4, 3, 7, ...). These sequences exhibit pseudo-random behaviour and generally terminate in a handful of cycles, properties reminiscent of 3x+1 and related sequences. We examine the elementary properties of these 'subprime' Fibonacci sequences.

18 pages, 5 figures

Related Organizations

Harvard University
United States
Massachusetts Institute of Technology
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University of Calgary
Canada

Keywords

11B75, Mathematics - Number Theory, FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO)

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