Kuznetsov's Sequence Kuznetsov's Sequence
(I made the name up, don't bother with Wikipedia or Google)

Given any number n &gt; 0, let r represent the reverse of the number n. Iterate until the final result is zero, passing the result of each iteration back into the function using recursion or a methodology of your choice by performing the below operation:

If r &gt; n for that iteration the result is r % n.
If n &gt; r for that iteration the result is n % r.
If n % r = 0 or r % n = 0, you terminate iteration.

Take the intermediate result of each execution and store them in an array for the final answer. The initial number n is not part of the sequence, nor is 0; the examples should make everything a little more obvious.
Lets walk through an example where n=32452345.
54325423 % 32452345 = 21873078 # r &gt; n, uses r % n
87037812 % 21873078 = 21418578 # r &gt; n, uses r % n
87581412 % 21418578 = 1907100  # r &gt; n, uses r % n
1907100 % 17091 = 9999         # n &gt; r, uses n % r
9999 % 9999 = 0                # r % n = n % r = 0, terminated

Result: [21873078, 21418578, 1907100, 9999]     

Another example n=12345678:
87654321 % 12345678 = 1234575 # r &gt; n, uses r % n
5754321 % 1234575 = 816021    # r &gt; n, uses r % n
816021 % 120618 = 92313       # n &gt; r, uses n % r
92313 % 31329 = 29655         # n &gt; r, uses n % r
55692 % 29655 = 26037         # r &gt; n, uses r % n
73062 % 26037 = 20988         # r &gt; n, uses r % n
88902 % 20988 = 4950          # r &gt; n, uses r % n
4950 % 594 = 198              # n &gt; r, uses n % r
891 % 198 = 99                # r &gt; n, uses r % n
99 % 99 = 0                   # r % n = n % r = 0, terminated

Result: [1234575, 816021, 92313, 29655, 26037, 20988, 4950, 198, 99]

A final example n=11000:
11000 % 11 = 0 # n % r = 0, terminated

Result: []

This is code-golf lowest byte-count wins.
PowerShell v2+, 89 bytes

param($n)for(){$r=-join"$n"["$n".length..0];if(!($n=(($r%$n),($n%$r))[$n-gt$r])){exit}$n}


Iterative solution. Lengthy because there's no easy way to reverse an array, so we stringify it and index on it backwards to store into $r. Then a pseudo-ternary to pull out the appropriate modulo and re-store into $n for the next round. However, if the result is zero, that means the !($n...) will be $true, so we exit instead of $n. The numbers are left on the pipeline and (implicitly) returned as an array, but without an encapsulating pipeline or saving the results into a variable, the default Write-Output sticks a newline between.

Try it online! (Yes, dead serious.)
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