2016/09/19 by Domingo Gómez‐Pérez, Gómez-Pérez, Domingo, Igor E. Shparlinski +1
Mathematics · Computer Science · #Rings, Modules, and Algebras #Computability, Logic, AI Algorithms #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.1609.05950
Recently, there has been a sharp rise of interest in properties of digits\nprimes. Here we study yet another question of this kind. Namely, we fix an\ninteger base g \≥ 2 and then for every infinite sequence
mathcal D =\n
di
i=0^
infty
in
0,
ldots, g-1
^
infty of g-ary digits we\nconsider the counting function varpi_ mathcal D,g(N) of integers n \≤\nN for which \∑i=0n-1 di gi is prime.\n We construct sequences mathcal D for which varpi_ mathcal D,g(N)\ngrows fast enough, and show that for some constant \ϑg< g there are\nat most O(\ϑgN) initial elements (d0, \…, dN-1) of\n mathcal D for which varpi_ mathcal D,g(N)=N+O(1). We also discuss\njoint arithmetic properties of integers and mirror reflections of their g-ary\nexpansions.\n