Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Walking to Infinity Along Some Number Theory sequences   An interesting open conjecture asks whether it is possible to walk to
infinity along primes, where each term in the sequence has one digit more than
the previous. We present different greedy models for prime walks to predict the
long-time behavior of the trajectories of orbits, one of which has similar
behavior to the actual backtracking one. Furthermore, we study the same
conjecture for square-free numbers, which is motivated by the fact that they
have a strictly positive density, as opposed to primes. We introduce stochastic
models and analyze the walks' expected length and frequency of digits added.
Lastly, we prove that it is impossible to walk to infinity in other important
number-theoretical sequences or on primes in different bases.

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The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an