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Hürlimann, W (2015)

A first digit theorem for powerful integer powers

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.

@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 = {}, }

Reference Type: Journal Article

Subject Area(s): Number Theory