An Unusual Continued Fraction

Badziahin, D.; Shallit, J.

doi:10.1090/proc/12848

An Unusual Continued Fraction

Badziahin, D.; Shallit, J.

Authors

D. Badziahin

J. Shallit

Abstract

We consider the real number σ with continued fraction expansion [a0, a1, a2,...] = [1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16,...], where ai is the largest power of 2 dividing i + 1. We show that the irrationality measure of σ2 is at least 8/3. We also show that certain partial quotients of σ2 grow doubly exponentially, thus confirming a conjecture of Hanna and Wilson.

Citation

Badziahin, D., & Shallit, J. (2016). An Unusual Continued Fraction. Proceedings of the American Mathematical Society, 144(5), 1887-1896. https://doi.org/10.1090/proc/12848

Journal Article Type	Article
Acceptance Date	May 24, 2015
Online Publication Date	Sep 15, 2015
Publication Date	May 1, 2016
Deposit Date	Jun 23, 2015
Publicly Available Date	Jun 26, 2015
Journal	Proceedings of the American Mathematical Society
Print ISSN	0002-9939
Electronic ISSN	1088-6826
Publisher	American Mathematical Society
Peer Reviewed	Peer Reviewed
Volume	144
Issue	5
Pages	1887-1896
DOI	https://doi.org/10.1090/proc/12848
Related Public URLs	http://arxiv.org/abs/1505.00667

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Copyright Statement
© 2015 American Mathematical Society. First published in Proceedings of the American Mathematical Society, 144 (2016), 1887-1896, published by the American Mathematical Society.