Consider the sequence
Form a new sequence, whose terms consist of the difference of the above sequence.
Repeat the process with the terms of this new sequence. When this is done sufficiently many times, you will eventually get the sequence
$$24, 24, 24, 24, \ldots$$
Why is this the case fundamentally, from a mathematical perspective? Why 24 exactly? I suspect it might have something to do with the fact that $24 = 4!$, though this could be completely off. Will it still work if we used the same algorithm with any arbitrary exponent $n$ instead of $4$? I can not answer this question because I can't seem to formalize this process in a way that allows me to see obvious convergence to a constant sequence.