SpringerPlus (2015) 4: 576.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.1186/s40064-015-1370-3

- For online information, click here.

**Abstract:** For any fixed power exponent, it is shown that the first digits of powerful integer powers follow a generalized Benford law (GBL) with size-dependent exponent that converges asymptotically to a GBL with the inverse double power exponent. In particular, asymptotically as the power goes to infinity these sequences obey Benford’s law. Moreover, the existence of a one-parametric size-dependent exponent function that converges to these GBL’s is established, and an optimal value that minimizes its deviation to two minimum estimators of the size-dependent exponent is determined. The latter is undertaken over the finite range of powerful integer powers less than 10^(s-m), m=8,…,15, where s=1,2,3,4,5 is a fixed power exponent.

**Bibtex:**

```
@article {,
AUTHOR = {Werner H{\"u}rlimann},
TITLE = {First digit counting compatibility for Niven integer powers},
JOURNAL = {SpringerPlus},
YEAR = {2015},
VOLUME = {4},
PAGES = {576},
DOI = {10.1186/s40064-015-1370-3},
URL = {http://link.springer.com/article/10.1186/s40064-015-1370-3},
}
```

**Reference Type:** Journal Article

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