2016/03/14 by Vladimir Shevelev, Shevelev, Vladimir
Computer Science · Mathematics · #11B83 #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1603.04434
openalex publication_date 2016/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and study two analogs of one of the best known sequence in Mathematics : Thue-Morse sequence. The first analog is concerned with the parity of number of runs of 1's in the binary representation of nonnegative integers. The second one is connected with the parity of number of 1's in the representation of nonnegative integers in so-called negabinary (or in base -2). We give for them some recurrent and structure formulas and prove that the second (0,1)-sequence is cube-free, while the first one is quint-free. Finally we consider several interesting unsolved problems.