Repdigit Keith numbers
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A Keith number is a positive integer N with the decimal representation a1a2⋯ak such that k ≥ 2 and N appears in the sequence that starts with a1, a2,…, ak 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.
KeywordsKeith number generalized Fibonacci recurrence repdigits
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