Journal of Integer Sequences, Vol. 23 (2020), Article 20.10.7

On the Erdős-Sloane and Shifted Sloane Persistence Problems


Gabriel Bonuccelli, Lucas Colucci, and Edson de Faria
Instituto de Matemática e Estatística
Universidade de São Paulo
São Paulo
Brazil

Abstract:

In this paper, we investigate two variations on the so-called persistence problem of Sloane: the shifted version, which was introduced by Wagstaff; and the nonzero version, proposed by Erdős. We explore connections between these problems and a recent conjecture of de Faria and Tresser regarding equidistribution of the digits of some integer sequences and a natural generalization of it.


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(Concerned with sequences A031346 A036461 A335808 A335824.)


Received September 1 2020; revised versions received October 14 2020; October 16 2020; October 18 2020. Published in Journal of Integer Sequences, October 18 2020.


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