  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.
