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Curious Continued Fractions, Nonlinear Recurrences and Transcendental Numbers

Hone, Andrew N.W. (2015) Curious Continued Fractions, Nonlinear Recurrences and Transcendental Numbers. Journal of Integer Sequences, 18 (15.8.4). pp. 1-10. ISSN 1530-7638. (KAR id:50523)

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https://cs.uwaterloo.ca/journals/JIS/VOL18/Hone/ho...

Abstract

We consider a family of integer sequences generated by nonlinear recurrences of the second order, which have

the curious property that the terms of the sequence, and integer multiples of the ratios of successive terms (which are also integers), appear interlaced in the continued fraction expansion of the sum of the reciprocals of the terms. Using the rapid (double exponential) growth of the terms, for each sequence it is shown that the sum of the reciprocals is a transcendental number.

Item Type: Article
Projects: [UNSPECIFIED] Cluster algebras with periodicity and discrete dynamics over finite fields
Uncontrolled keywords: Continued fraction, nonlinear recurrence, transcendental number, Laurent property.
Subjects: Q Science > QA Mathematics (inc Computing science) > QA150 Algebra > QA241 Number theory
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Andrew Hone
Date Deposited: 16 Sep 2015 23:16 UTC
Last Modified: 16 Feb 2021 13:28 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/50523 (The current URI for this page, for reference purposes)
Hone, Andrew N.W.: https://orcid.org/0000-0001-9780-7369
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