Counting Keith Numbers
Department of Applied Mathematics and
Institute for Theoretical Computer Science (ITI)
Faculty of Mathematics and Physics
Malostranské nám. 25
Instituto de Matemáticas
Universidad Nacional Autonoma de México
A Keith number is a positive integer N with decimal
such that n >= 2 and N
appears in the sequence
(Km)m >= 1
given by the
recurrence K1 = a1, ... ,
Kn = an and
Km-2 + ... +
for m > n.
We prove that there are only finitely many Keith numbers using only one
decimal digit (i.e.,
a2= ... =
and that the set of Keith numbers is of asymptotic density zero.
Full version: pdf,
(Concerned with sequence
Received September 21 2006;
revised version received January 16 2007.
Published in Journal of Integer Sequences January 17 2007.
Journal of Integer Sequences home page