Allan,in the Index to the OEIS there is this entry self-describing numbers, sequences related to : [edit <https://oeis.org/w/index.php?title=Index_to_OEIS:_Section_Se&action=edit§ion=3> ]self-describing numbers: Autobiographical numbers: A047841 <http://oeis.org/A047841> (A104784 <http://oeis.org/A104784> is an erroneous version), self-describing primes: A108810 <http://oeis.org/A108810>, semiprimes: A173101 <http://oeis.org/A173101>, not complete information: A059504 <http://oeis.org/A059504>, primes therein: A109775 <http://oeis.org/A109775>, self descriptive (possibly redundant) numbers: A109776 <http://oeis.org/A109776> It may be that your variant is new - please add it & update the Index entry too! Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Tue, Oct 22, 2019 at 4:52 PM Allan Wechsler <acwacw@gmail.com> wrote:
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. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun