Geodesic
Counting Keith numbers
Journal of integer sequences, Tome 10 (2007) no. 2.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A Keith number is a positive integer $N$ with decimal representation $a_{1} a_{2} \dots a_{n}$ such that $n >= 2$ and $N$ appears in the sequence $(K_{m})_{m >= 1}$ given by the recurrence $K_{1} = a_{1}, \dots , K_{n} = a_{n}$ and $K_{m} = K_{m-1} + K_{m-2} + \dots + K_{m-n}$ for $m > n$. We prove that there are only finitely many Keith numbers using only one decimal digit (i.e., $a_{1}= a_{2}= \dots = a_{n}$), and that the set of Keith numbers is of asymptotic density zero.
Classification : 11B39, 11A63
Keywords: keith number, density, generalized Fibonacci recurrence 
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     author = {Klazar, Martin and Luca, Florian},
     title = {Counting {Keith} numbers},
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     number = {2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_2_a1/}
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Klazar, Martin; Luca, Florian. Counting Keith numbers. Journal of integer sequences, Tome 10 (2007) no. 2. http://geodesic.mathdoc.fr/item/JIS_2007__10_2_a1/