Counting Keith numbers
Number Theory
2007-05-23 v1 Combinatorics
Abstract
A Keith number is a positive integer N with the decimal representation a_1a_2...a_n such that n>=2 and N appears in the sequence (K_m) given by the recurrence K_1=a_1,...,K_n=a_n and K_m=K_{m-1}+K_{m-2}+...+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=...=a_n), and that the set of Keith numbers is of asymptotic density zero.
Cite
@article{arxiv.math/0608419,
title = {Counting Keith numbers},
author = {Martin Klazar and Florian Luca},
journal= {arXiv preprint arXiv:math/0608419},
year = {2007}
}
Comments
12 pages