Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Collatz Cycles and $3n+c$ Cycles   Halbeisen and Hungerbuhler determined optimal bounds for the length of
rational Collatz cycles. Their methods are extended to $3n+c$ cycles. Another
sequence having properties similar to those of Riemann zeta function zeros is
introduced.

9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas