Abstract
Number 197 is contained in the sequence 1, 9, 7, 17, 33, 57, 107, 197, 361, ... Numbers with this property, such as 14, 19, 28, 47, 61, 75, 197, 742, ..., are called Keith numbers. It is not known if there are infinitely many of them.
We prove that there are only finitely many Keith numbers using just one decimal digit and that the set of Keith numbers has density zero.