All the Xenodromes

Pyth, 8 bytes

f{IjTQU^

Filters the numbers in [0, n^n - 1] on having no duplicate elements in base n. The base conversion in Pyth will work with any base, but since this looks at a very quickly increasing list of numbers, it will eventually be unable to store the values in memory.

Try it online!

Explanation:

f{IjTQU^QQ    - Auto-fill variables
      U^QQ    - [0, n^n-1]
f             - keep only those that ...
 {I           - do not change when deduplicated
   jTQ        - are converted into base n

Jelly, 9 8 bytes

ð*ḶbQ€Qḅ

Thanks to @JonathanAllan for golfing off 1 byte!

Try it online! or verify all test cases.

How it works

ð*ḶbQ€Qḅ  Main link. Argument: n

ð         Make the chain dyadic, setting both left and right argument to n.
          This prevents us from having to reference n explicitly in the chain.
 *        Compute nⁿ.
  Ḷ       Unlength; yield A := [0, ..., nⁿ - 1].
   b      Convert each k in A to base n.
    Q€    Unique each; remove duplicate digits.
      Q   Unique; remove duplicate digit lists.
       ḅ  Convert each digit list from base n to integer.

Python 2, 87 bytes

n=input()
for x in range(n**n):
 s={n};a=x
 while{a%n}|s>s:s|={a%n};a/=n
 print-~-a*`x`

Prints extra blank lines for non-xenodromes:

golf % python2.7 xenodromes.py <<<3
0
1
2
3

5
6
7



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