Type: Article

Repdigit Keith numbers

Bravo, Jhon J.; Guzman, Sergio; Luca, Florian;

Abstract:

A Keith number is a positive integer N with the decimal representation a (1) a (2)a <-a (k) such that k a parts per thousand yen 2 and N appears in the sequence that starts with a (1), a (2),aEuro broken vertical bar, a (k) and for which each term afterwards is the sum of the k preceding terms. In 2007, Klazar and Luca [M. Klazar and F. Luca, Counting Keith numbers, J. Integer Seq., 10(2):Article 07.2.2, 2007] proved that there are only finitely many Keith numbers with only one distinct digit (so-called repdigits). In this paper, we prove that there are no Keith numbers which are repdigits.