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Denominator sequences of continued fractions II

Published online by Cambridge University Press:  09 April 2009

R. T. Worley
R. T. Worley
Affiliation:
Monash UniversityClayton, Victoria, 3168 Australia
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In part I, I considered the problem of discovering when, given an irrational α which has a simple continued fraction representation with convergents pn/qn, there exists α' for which the denominator sequence for convergents is a subsequence of (qn). It was shown that such an α' exists if the continued fraction representation was “nearly periodic” with odd period. The following is a generalization of the results of part I to semi-regular continued fractions, where the problem seems to fit more naturally.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 4 , June 1973 , pp. 470 - 475
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Perron, O., Die Lehre von den Kettenbrüchen (Chelsea).Google Scholar
[2]Worley, R. T., ‘Denominator Sequences of Continued Fractions I’, Aust. Math. Soc. 15 (1973), 112–116.CrossRefGoogle Scholar