Communications in Mathematics and Applications 5(3), pp. 91-99.

**ISSN/ISBN:** 0975-8607
**DOI:** Not available at this time.

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**Abstract:** For any fixed power exponent, it is shown that the first digits of powers from perfect power numbers follow a generalized Benford law (GBL) with size-dependent exponent that converges asymptotically to a GBL with half of the inverse power exponent. In particular, asymptotically as the power goes to infinity these first digit sequences obey Benford's law. Moreover, we show the existence of a one-parametric size-dependent exponent function that converge to these GBL's and determine an optimal value that minimizes its deviation to two minimum estimators of the size-dependent exponent over the finite range of powers from perfect power numbers less than $10^{5m \cdot s}$, $m = 2,\ldots,6$, where $s = 1,2,3,4,5$ is a fixed power exponent.

**Bibtex:**

```
@article {,
AUTHOR = {Werner H{\"u}rlimann},
TITLE = {A first digit theorem for powers of perfect powers},
JOURNAL = {Communications in Mathematics and Applications},
YEAR = {2014},
VOLUME = {5},
NUMBER = {3},
PAGES = {91--99},
URL = {http://www.rgnpublications.com/journals/index.php/cma/article/view/253},
}
```

**Reference Type:** Journal Article

**Subject Area(s):** Number Theory