SpringerPlus (2015) 4: 576.
ISSN/ISBN: Not available at this time. DOI: 10.1186/s40064-015-1370-3
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