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Corpus ID: 225094200

Walking to Infinity Along Some Number Theory sequences

@article{Miller2020WalkingTI,
title={Walking to Infinity Along Some Number Theory sequences},
author={Steven J. Miller and Fei 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 opposed… Expand

Update: This work reproduces an earlier result of Peck, which the author was initially unaware of. The method of the proof is essentially the same as the original work of Peck. There are no new… Expand

The authors sharpen a result of Baker and Harman (1995), showing that [x, x + x0.525] contains prime numbers for large x. An important step in the proof is the application of a theorem of Watt (1995)… Expand

Preface. List of Symbols. Leonardo Fibonacci. The Rabbit Problem. Fibonacci Numbers in Nature. Fibonacci Numbers: Additional Occurrances. Fibonacci and Lucas Identities. Geometric Paradoxes.… Expand

This paper discusses stochastic models for predicting the long-time behavior of the trajectories of orbits of the 3x+1 problem and, for comparison, the 5x+1 problem. The stochastic models are… Expand