Non-regularity of floor(alpha + log_k(n))
Number Theory
2010-03-15 v2
Abstract
This paper presents a new proof that if k^alpha is irrational then the sequence floor(alpha + log_k(n)) is not k-regular. Unlike previous proofs, the methods used do not rely on automata or language theoretic concepts. The paper also proves the stronger statement that if k^\alpha is irrational then the generating function in k non-commuting variables associated with floor(alpha + log_k(n)) is not algebraic.
Cite
@article{arxiv.0906.0058,
title = {Non-regularity of floor(alpha + log_k(n))},
author = {Eric S. Rowland},
journal= {arXiv preprint arXiv:0906.0058},
year = {2010}
}
Comments
4 pages; published version