Pure Mathematical Sciences 3(3), pp. 129 - 139.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.12988/pms.2014.4615

- For online information, click here.

**Abstract:** For any fixed integer power, it is shown that the first digits of square-free integer powers follow a generalized Benford law (GBL) with size-dependent exponent that converges asymptotically to a GBL with inverse power exponent. In particular, asymptotically as the power goes to infinity the sequences of square-free integer powers 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 square-free integer powers less than 10 s⋅m , m = 4,...,10 , where s = 1,2,3,4,5,10 is a fixed integer power.

**Bibtex:**

```
@article {,
AUTHOR = {Werner H{\"u}rlimann},
TITLE = {First digit counting compatibility for Niven integer powers},
JOURNAL = {Pure Mathematical Sciences},
YEAR = {2014},
VOLUME = {3},
NUMBER = {3},
PAGES = {129--139},
DOI = {10.12988/pms.2014.4615},
URL = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.683.5799&rep=rep1&type=pdf},
}
```

**Reference Type:** Journal Article

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