Corpus ID: 225094200

Walking to Infinity Along Some Number Theory sequences

  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},
  • S. J. Miller, F. Peng, +3 authors The Polymath Reu Program
  • Published 2020
  • Mathematics
  • arXiv: Number Theory
  • 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… CONTINUE READING

    Tables from this paper


    The Difference Between Consecutive Primes, II
    • 383
    • PDF
    On the difference between consecutive primes
    • 186
    • PDF
    Fibonacci and Lucas Numbers with Applications
    • 1,013
    Stochastic Models for the 3x+1 and 5x+1 Problems
    • 11
    • PDF
    Beyond pair correlation
    • 37
    • PDF
    Miller and R
    • Takloo-Bighash,An Invitation to Modern Number Theory, Princeton University Press,
    • 2006
    Takloo-Bighash, An Invitation to Modern Number
    • 2006
    Beyond pair correlation, Paul Erdős and his mathematics
    • Vol. I (Budapest,
    • 1999