Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two analogs of Thue-Morse sequence   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.

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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex