Abstract
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 loglcm(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.
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