2021/08/08 by Sanna, Carlo
#11B39 (Primary) 11B37 #11N37 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR)
paper · doi:10.48550/arxiv.2108.03628
Let (Ln)n ≥ 1 be the sequence of Lucas numbers, defined recursively by L1 := 1, L2 := 3, and Ln + 2 := Ln + 1 + Ln, for every integer n ≥ 1. We determine the asymptotic behavior of log lcm (L1 + s1, L2 + s2, …, Ln + sn) as n → +∞, for (sn)n ≥ 1 a periodic sequence in \-1, +1\. We also carry out the same analysis for (sn)n ≥ 1 a sequence of independent and uniformly distributed random variables in \-1, +1\. These results are Lucas numbers-analogs of previous results obtained by the author for the sequence of Fibonacci numbers.