[seqfan] Post's tag system

Neil Sloane njasloane at gmail.com
Sun Jul 30 01:05:20 CEST 2017

Post's tag system is described in A284116.  (I learned about it from
reading John Stillwell's wonderful book "Elements of Mathematics: From
Euclid to Goedel", Princeton, 2016). There are some vague similarities
between the Post tag construction and the Curling Number Conjecture
(see arXiv:1212.6102), which might give a hint as to why the latter has
proved so intractable.

In particular, the known terms of A284116 are a bit similar to those of
A094004 (compare the two graphs), so it would be interesting to
have a lot more terms of the former sequence, in case people would like to

It would be nice also to have a lot more terms for the other sequences
related to Post tag systems that I added today (A289670-A289674).

Rather than trying to prove the Curling Number Conjecture, maybe it would
be easier to show it is equivalent to one of the unsolvable problems
(studied by Post, Turing, ...) in the field of computability!  ("I can't
solve the problem, so instead I'll show that the problem is insoluble".)

By the way, my Maple program in A289670 is very naive, and I included it
merely to show how I found the terms.
All of these entries - especially A284116 - could use high-quality programs
- and a lot more terms.

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