Non-regularity of floor(alpha + logk(n))
Abstract
This paper presents a new proof that if kalpha is irrational then the sequence floor(alpha + logk(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 kα is irrational then the generating function in k non-commuting variables associated with floor(alpha + logk(n)) is not algebraic.
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