Here is a Perl regular expression using Perl 5.10 extensions (this is a finite state automaton):
^(?&s)(?(DEFINE) (?<s>([0369](?&z)|[147](?&j)|[258](?&d))) (?<z>($|[0369](?&z)|[147](?&j)|[258](?&d))) (?<j>([0369](?&j)|[147](?&d)|[258](?&z))) (?<d>([0369](?&d)|[147](?&z)|[258](?&j)))) </d></j></z></s>
