Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A Khinchin Sequence

Author: Thomas Wieting
Journal: Proc. Amer. Math. Soc. 136 (2008), 815-824
MSC (2000): Primary 11Y65; Secondary 28D05
Published electronically: November 30, 2007
MathSciNet review: 2361853
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Abstract: We prove that the geometric and harmonic means of the sequence $ Z_2$ of positive integers proposed by Bailey, Borwein, and Crandall converge to the corresponding Khinchin Constants.

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Additional Information

Thomas Wieting
Affiliation: Department of Mathematics, Reed College, Portland, Oregon 97202

Keywords: Khinchin Sequence, continued fraction expansion, geometric mean, harmonic mean
Received by editor(s): January 12, 2007
Published electronically: November 30, 2007
Additional Notes: Thanks to R. C. Crandall for suggesting the subject of this paper.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.