# sequences that are permutations

N. J. A. Sloane njas at research.att.com
Sat Oct 13 21:45:14 CEST 2001

```Howard Landman <howard at polyamory.org> has put together a preliminary
list of the sequences that are permutations of the natural numbers
(or in some cases of the nonnegative integers).

Here is the current version.  If anyone knows of other examples,
please send them to me (njas).

The entries in the index will also be updated.

Sequence-Inverse
A000027	- self-inverse
A002251	- self-inverse
A003100	- self-inverse
A003188	- A006068
A004484	- A064206
A004485	- A064207
A004486	- A064208
A004487	- A064211
A019444	- self-inverse
A026243	- self-inverse
A029654	- A064360
A064413 - A064664
A032447	- A064275
A035312	- A035358
A035506	- A064357
A035513	- A064274
A047708	- A048850
A048647	- A064212
A048672	- A064273
A048673	- A064216
A048679	- A048680
A052330	- A064358
A059900 - A059884
A052331	- A064359
A054238	- A054239
A054424	- A054426
A054427	- A054428
A054429	- self-inverse
A054430	- self-inverse
A054081	- n/a		array: rows are permutations but it isn't itself

I think the squares of these permutations also should be in the database.
I suggested this to Howard, but this is a big job and if anyone else would
be willing to send in some "squares" that would be very helpful.

If f is one of the permutations mentioned above
then what I mean is the sequence
f(f(1)), f(f(2)), f(f(3)), f(f(4)), ...
- except perhaps beginning with f(f(0)) if that is appropriate.

Of course many of these may already be in the database; if so this should be noted.

Neil Sloane

```