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Volume 11
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10.3390/math11020455
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Article

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

by
Alaa Altassan
1 and
Murat Alan
2,*
1
Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2
Department of Mathematics, Yildiz Technical University, Istanbul 34210, Turkey
*
Author to whom correspondence should be addressed.
Mathematics 2023, 11(2), 455; https://doi.org/10.3390/math11020455
Submission received: 2 December 2022 / Revised: 8 January 2023 / Accepted: 10 January 2023 / Published: 14 January 2023
(This article belongs to the Special Issue Algebraic, Analytic, and Computational Number Theory and Its Applications)
Versions Notes

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 k-Fibonacci numbers; repdigits; almost repdigits; linear forms in logarithms; MR imaging; tiny golden angles; k-generalized tiny golden angles

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MDPI and ACS Style

Altassan, A.; Alan, M. Almost Repdigit k-Fibonacci Numbers with an Application of k-Generalized Fibonacci Sequences. Mathematics 2023, 11, 455. https://doi.org/10.3390/math11020455

AMA Style

Altassan A, Alan M. Almost Repdigit k-Fibonacci Numbers with an Application of k-Generalized Fibonacci Sequences. Mathematics. 2023; 11(2):455. https://doi.org/10.3390/math11020455

Chicago/Turabian Style

Altassan, Alaa, and Murat Alan. 2023. "Almost Repdigit k-Fibonacci Numbers with an Application of k-Generalized Fibonacci Sequences" Mathematics 11, no. 2: 455. https://doi.org/10.3390/math11020455

APA Style

Altassan, A., & Alan, M. (2023). Almost Repdigit k-Fibonacci Numbers with an Application of k-Generalized Fibonacci Sequences. Mathematics, 11(2), 455. https://doi.org/10.3390/math11020455

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