Dear Allan, Neil's link to the OEIS index leads to A047841 and A109776 which are close to your "census" map. I removed their tuples with zeroes, and with duplicates, sorted them by increasing digits, and checked (by a program) whether they are fixed points under the census map. If I got it right, then I think that the following ones marked with "*" are new: 2,1, 3,2, 2,3, 1,K (K>3) 2,2 3,1, 1,2, 3,3, 1,A (A>3) *3,1, 2,2, 3,3, 1,A, 1,B (A>3, B>A) *3,1, 3,3, 1,A, 1,B (A>3, B>A) 4,1, 3,2, 2,3, 2,4, 1,A, 1,B, 1,C (A>4, B>A, C>B *5,1, 3,2, 2,3, 1,4, 2,5, 1,A, 1,B, 1,C (A>5, B>A, C>B) 5,1, 3,2, 2,3, 2,5, 1,A, 1,B, 1,C, 1,D *6,1, 3,2, 2,3, 1,4, 1,5, 2,6, 1,7, 1,8, 1,9 I imagine that your definition is different from several existing OEIS sequences because it is base-independant and does not count zero. I can only speculate whether there are more "template" tuples. Regards - Georg Am 23.10.2019 um 18:45 schrieb Neil Sloane:
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