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.