TY - JOUR
AU - HÃ¼rlimann, Werner
PY - 2014/12/31
Y2 - 2022/10/03
TI - A First Digit Theorem For Powers of Perfect Powers
JF - Communications in Mathematics and Applications
JA - Comm. Math. Appl.
VL - 5
IS - 3
SE - Research Article
DO - 10.26713/cma.v5i3.253
UR - http://www.rgnpublications.com/journals/index.php/cma/article/view/253
SP - 91-99
AB - For any fixed power exponent, it is shown that the first digits of powers from perfect power numbers follow a generalized Benford law (GBL) with size-dependent exponent that converges asymptotically to a GBL with half of the inverse power exponent. In particular, asymptotically as the power goes to infinity these first digit sequences 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 powers from perfect power numbers less than $10^{5m \cdot s}$, $m = 2,\ldots,6$, where $s = 1,2,3,4,5$ is a fixed power exponent.
ER -