Main Question or Discussion Point
I would like some direction on studying powers of integers and if they are in any way related to factorials. I was studying the sequence of cubics 1, 8, 27, 64, 125 and so. After a certain number of rounds of a basic rule I choose to apply to this sequence, I arrived at a new sequence where one particular integer (not 0 nor 1) was repeated. I tried a sequence of integers raised to fourth power and found that my process brought about similar results. Depending on the exponent ( natural number ) used on the integers that I write out, I can now predict how many rounds it will take to get to the repeated integer and also predict that the repeated integer is a certain factorial. I am not referring to 0! nor 1! Does this discovery for me seem important or useful to any branch of math? I am new at asking questions here; I enjoy patterns with numbers and am trying to write conjectures or maybe a theorem or two from my discoveries. thanks for the help .