Arithmetic properties of integers in chains and reflections of g-ary expansions

Domingo Gómez-Pérez, Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Recently, there has been a sharp rise of interest in properties of digits primes. Here we study yet another question of this kind. Namely, we fix an integer base g ⩾ 2 and then for every infinite sequence

D={di}i=0 ∈ {0,..., g - 1}

of g-ary digits we consider the counting function ωD,g(N) of integers n ⩽ N for which ∑n − 1 i = 0digi is prime. We construct sequences for which ωD,g(N) grows fast enough, and show that for some constant ϑg < g there are at most O(ϑN g) initial elements (d0, …, dN − 1) of D for which ωD,g(N) = N + O(1). We also discuss joint arithmetic properties of integers and mirror reflections of their g-ary expansions.

Original languageEnglish
Pages (from-to)184-192
Number of pages9
JournalExperimental Mathematics
Volume27
Issue number2
Early online date31 Oct 2016
DOIs
Publication statusPublished - 2018
Externally publishedYes

Keywords

  • digits
  • primes
  • SUM

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