Non-regularity of floor(alpha + log_k(n))

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^αis irrational then the generating function in k non-commuting variables associated with floor(alpha + log_k(n)) is not algebraic.

4 pages; published version