The k-Generalized Lucas Numbers Close to a Power of 2

AÇIKEL A., Irmak N., Szalay L.

Mathematica Slovaca, vol.73, no.4, pp.871-882, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 73 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.1515/ms-2023-0064
  • Journal Name: Mathematica Slovaca
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.871-882
  • Keywords: Baker method, k-generalized Lucas sequence, LLL reduction
  • Hatay Mustafa Kemal University Affiliated: Yes

Abstract

Let k ≥ 2 be a fixed integer. The k-generalized Lucas sequence {Ln(k)}n≥0 starts with the positive integer initial values k, 1, 3, ⋯, 2k-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 |