From: utzoo!decvax!ucbvax!G:shallit
Newsgroups: net.math
Title: Re: numeros lindos
Article-I.D.: populi.212
Posted: Tue Jun 22 10:02:47 1982
Received: Sun Jun 27 02:10:22 1982

The problem is very well-known.  These numbers are sometimes called
"automorphic" numbers in the literature.  Martin Gardner has written
about them in his Mathematical Games column in Scientific American
(but I can't remember when).  If my memory is correct, it's not
hard to prove there are exactly 2 n-digit automorphs (in base 10) for
every n.  Their sum is 1+10^n.  Also, the Journal of Recreational
Mathematics has many articles on generalization to other bases, powers,
etc.