2020/04/15 by S. S. Rout, Rout, S. S., N. K. Meher +1
Computer Science · Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2004.06988
openalex publication_date 2020/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let S= \ p1, …, ps\ be a finite, non-empty set of distinct prime numbers and (Un)n ≥ 0 be a linear recurrence sequence of integers of order r. For any positive integer k, we define (Uj(k))j≥ 1 an increasing sequence composed of integers of the form Unk +⋯ + Un1, nk>⋯ >n1. Under certain assumptions, we prove that for any ε>0, there exists an integer n0 such that [Uj(k)]S < (Uj(k))ε, for j > n0, where [m]S denote the S-part of the positive integer m. On further assumptions on (Un)n ≥ 0, we also compute an effective bound for [Uj(k)]S of the form (Uj(k))1-c, where c is a positive constant depends only on (Un)n ≥ 0 and S.