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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| Official URL: https://cs.uwaterloo.ca/journals/JIS/VOL18/Hone/ho... |
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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 |
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| Projects: | 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 |
| Funders: | Organisations -1 not found. |
| Depositing User: | Andrew Hone |
| Date Deposited: | 16 Sep 2015 23:16 UTC |
| Last Modified: | 10 Dec 2022 20:56 UTC |
| Resource URI: | https://kar.kent.ac.uk/id/eprint/50523 (The current URI for this page, for reference purposes) |
University of Kent Author Information
Hone, Andrew N.W..
| Creator's ORCID: |
 https://orcid.org/0000-0001-9780-7369
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