Almost Repdigit k -Fibonacci Numbers with an Application of k -Generalized Fibonacci Sequences

Alaa Altassan and Murat Alan ()
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Alaa Altassan: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Murat Alan: Department of Mathematics, Yildiz Technical University, Istanbul 34210, Turkey

Mathematics, 2023, vol. 11, issue 2, 1-16

Abstract: In this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and we search all terms of the k -generalized Fibonacci sequence which are almost repdigits. In particular, we find all k -generalized Fibonacci numbers which are powers of 10 as a special case of almost repdigits. In the second part of the paper, by using the roots of the characteristic polynomial of the k -generalized Fibonacci sequence, we introduce k -generalized tiny golden angles and show the feasibility of this new type of angles in application to magnetic resonance imaging.

Keywords: k -Fibonacci numbers; repdigits; almost repdigits; linear forms in logarithms; MR imaging; tiny golden angles; k -generalized tiny golden angles (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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