Arithmetic Properties of Integers in Chains and Reflections of g-ary Expansions

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 sequenceof g-ary digits we consider the counting function D,g (N ) of integers n N for whichWe construct sequences D for which D,g (N ) grows fast enough, and show that for some constant ϑ g < g there are at most O(ϑWe also discuss joint arithmetic properties of integers and mirror reflections of their g-ary expansions.

The arithmetic of consecutive polynomial sequences over finite fields

“…The rest of the section is dedicated to obtaining a formula for I 2 and explicit lower bounds for I 3 and I 4 , which are better than those implied in [4]. Finally, we want to remark that analogues of our results can be considered for sequences of g-ary digits, g 2; see [10]. More precisely, given a sequence of g-ary digits {d n } n 0 , d n ∈ {0, 1, .…”