The normality of digits in almost constant additive functions
Number Theory
2012-06-07 v1
Abstract
We consider numbers formed by concatenating some of the base b digits from additive functions f(n) that closely resemble the prime counting function \Omega(n). If we concatenate the last \lceil y \frac{\log \log \log n}{\log b} \rceil digits of each f(n) in succession, then the number so created will be normal if and only if 0 < y \le 1/2. This provides insight into the randomness of digit patterns of additive function after the Erdos-Kac theorem becomes ineffective.
Cite
@article{arxiv.1206.1095,
title = {The normality of digits in almost constant additive functions},
author = {Joseph Vandehey},
journal= {arXiv preprint arXiv:1206.1095},
year = {2012}
}