Let us consider the sequence. 1, 11,21, 1211, 111221, ... , where each term is the reading (by a machine) of the preceding one: 11 means "once one", i.e., the reading of the first term; 21 means "twice one", i.e., the reading of the second term; 1211 means "once two once one", i.e., the reading of the third term, etc. Given a positive integer a, its successive readings r(a), r(r(a)), ... leads to an infinite sequence s(a) of positive integers.