I am sure this has been discussed here before, so if somebody just has a pointer to any previous discussion, let me know. Suppose we have a finite sequence of non-negative integers. We can create a new sequence that is a "census" of the first. For example, the census of (1,4,1,4,2,1,3) is (3,1,1,2,1,3,2,4) -- that is, three 1's, one 2, one 3, and two 4's. I am interested in any tuple that is its own census. A simple example is (2,2); a more complicated example is (2,1,3,2,2,3,1,K). The K can be replaced with any number bigger than 3. I found another class of examples of the form (K,1,3,2,2,3,2,K,1,A,1,B...) where K,A,B... are distinct from each other and bigger than 3, and there are exactly K-1 terms in the A,B... set. Let's declare that the choice of the value of singletons doesn't matter. I have an intuition that the number of types of self-censusing sequences is quite small -- maybe only the three types I just mentioned? Or did I miss a few? I would not be surprised if I did, but I would be surprised if there were a _lot_ more types.