Does some mathematician knows if the above fulguration I had is a known fact?
Yeah, fortunately! That succession of powers is the base of the positional notation used to represent numbers!
So, what do you get when you subtract 1 to a power or 10? a string of nines. What do you get when you do the same to a power of 16 in hexadecimal? a string of F's. What do you get when you subtract one to a power of 2 in binary? a string of ones.
9000 = 9 * 1000 = (10 - 1) * 10 ** 3
900 = 9 * 100 = (10 - 1) * 10 ** 2
90 = 9 * 10 = (10 - 1) * 10 ** 1
+ 9 = 9 * 1 = (10 - 1) * 10 ** 0
9999 = 9 * 1111 = (10 - 1) * 1111
10000 = 10 ** 4
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