# Walking to Infinity Along Some Number Theory sequences

@article{Miller2020WalkingTI, title={Walking to Infinity Along Some Number Theory sequences}, author={S. J. Miller and F. Peng and Tudor Popescu and Joshua M. Siktar and Nawapan Wattanawanichkul and The Polymath Reu Program}, journal={arXiv: Number Theory}, year={2020} }

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 opposedâ€¦Â CONTINUE READING

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