On the l.c.m. of shifted Lucas numbers

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 asymptotic behavior loglcm(L1+s1,L2+s2,…,Ln+sn) as n→+∞, (sn)n≥1 a periodic in {−1,+1}. also carry out same analysis independent uniformly distributed random variables These results are numbers-analogs previous obtained author Fibonacci numbers.