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

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

2009-05-30

arxiv.org/abs/0906.0058v2

Integers 10 (2010) 19-23

Mathematics

Number Theory

4 pages; published version

Scientific paper

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.

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