Arithmetic Properties of Integers in Chains and Reflections of g-ary Expansions. Issue 2 (3rd April 2018)

• Record Type: Journal Article
• Authors: Gómez-Pérez, Domingo; Shparlinski, Igor E.
• Is Part Of: Experimental mathematics. Volume 27:Issue 2(2018)
• Page Start: 184
• Page End: 192
• Publication Date: 2018-04-03
• Subjects: digits -- primes; 11A41 -- 11A63 -- 11N05; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2016.1239146
• Languages: English
• ISSNs: 1058-6458

Abstract

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