Acikel, AbdullahIrmak, NurettinSzalay, Laszlo2024-09-182024-09-1820230139-99181337-2211https://doi.org/10.1515/ms-2023-0064https://hdl.handle.net/20.500.12483/10818Let k >= 2 be a fixed integer. The k-generalized Lucas sequence {L-n((k))}(n)>=(0) starts with the positive integer initial values k, 1, 3, ..., 2(k-1)-1, and each term afterward is the sum of the k consecutive preceding elements. An integer n is said to be close to a positive integer m if n satisfies |n-m| < root m. In this paper, we combine these two concepts. We solve completely the diophantine inequality |L-n((k)) - 2(m) | < 2(m/2) in the non-negative integers k, n, and m. This problem is equivalent to the resolution of the equation L-n((k)) = 2(m) + t with the condition |t| < 2(m/2), t is an element of Z. We also discovered a new formula for L-n((k)) which was very useful in the investigation of one particular case of the problem.eninfo:eu-repo/semantics/closedAccessk-generalized Lucas sequenceBaker methodLLL reductionArticle73487188210.1515/ms-2023-00642-s2.0-85168093054Q2WOS:001043701900005Q2