Almost Repdigit <i>k</i>-Fibonacci Numbers with an Application of <i>k</i>-Generalized Fibonacci Sequences

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

• <i>k</i>-Fibonacci numbers
• repdigits
• almost repdigits
• linear forms in logarithms
• MR imaging
• tiny golden angles