Comptes Rendus de L'Academie Bulgare des Sciences, cilt.77, sa.1, ss.3-10, 2024 (SCI-Expanded)
Let k ≥ 2 be an integer and let (L(nk))n≥2−k be the k-generalized Lucas sequence with certain initial k terms and each term afterward is the sum of the k preceding terms. Mersenne numbers are the numbers of the form 2a−1, where a is any positive integer. The aim of this paper is to determine all Mersenne numbers which lie inside k-Lucas sequences.