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

Eric S. Rowland

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arXiv · 0906.0058

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

Eric S. Rowland

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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.

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BibTeX RIS

Eric S. Rowland. 2010-03-12. Non-regularity of floor(alpha + log_k(n)). https://arxiv.org/abs/0906.0058

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