Okay but what's the significance of (non-unity) powers of e? e is the optimum of a specific function[1], and you lose the benefits for higher values.
It's true that you can conveniently represent the numbers by using integer powers of the base (like representing binary with hexadecimal), but the whole reason e is a "good" base in the first place is because you're (partially) minimizing the number of distinct symbols needed to represent a number, and you lose that once you go to a higher base.
Plus, using a slightly-off integer like 7 breaks the integer-power-mapping anyway.
It's true that you can conveniently represent the numbers by using integer powers of the base (like representing binary with hexadecimal), but the whole reason e is a "good" base in the first place is because you're (partially) minimizing the number of distinct symbols needed to represent a number, and you lose that once you go to a higher base.
Plus, using a slightly-off integer like 7 breaks the integer-power-mapping anyway.
[1] x ^ (N/x) for any N.