Results

**1 - 1**of**1**### A First Digit Theorem for Powers

"... Abstract. 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 parameter that converges asymptotically to a GBL with half of the inverse power exponent. In particular, asymptotically as the pow ..."

Abstract
- Add to MetaCart

Abstract. 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 parameter 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-parameter size-dependent function that converges to the parameter of these GBL’s and determine an optimal value that minimizes its deviation to two minimum estimators of the size-dependent parameter over the finite range of powers from perfect power numbers less than 105m·s, m = 2,...,6, where s = 1,2,3,4,5 is a fixed power exponent.