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Hürlimann, W (2014)

A first digit theorem for square-free integer powers

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

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

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.

@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 = {}, }

Reference Type: Journal Article

Subject Area(s): Number Theory