Journal of Integer Sequences, Vol. 10 (2007), Article 07.5.1

Interspersions and Fractal Sequences Associated with Fractions cj/dk

Clark Kimberling
Department of Mathematics
University of Evansville
1800 Lincoln Avenue
Evansville, IN 47722


Suppose $c\geq 2$ and $d\geq 2$ are integers, and let $S$ be the set of integers $\left\lfloor c^j/d^k\right\rfloor$, where $j$ and $k$ range over the nonnegative integers. Assume that $c$ and $d$ are multiplicatively independent; that is, if $p$ and $q$ are integers for which $c^p=d^q,$ then $p=q=0$. The numbers in $S$ form interspersions in various ways. Related fractal sequences and permutations of the set of nonnegative integers are also discussed.

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(Concerned with sequences A007337 A022447 A114537 A114577 A120862 A120863 A124904 A124905 A124906 A124907 A124908 A124909 A124910 A124911 A124912 A124913 A124914 A124915 A124916 A124917 A124918 A124919 A125150 A125151 A125152 A125153 A125154 A125155 A125156 A125157 A125158 A125159 A125160 and A125161 .)

Received December 30 2006; revised version received May 4 2007. Published in Journal of Integer Sequences May 6 2007.

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