>From checking also powers of 3, I can't find more than c==5 (for 3**20 and 3**124).
אורי u...@speedy.net On Tue, Jan 4, 2022 at 7:24 AM אורי <u...@speedy.net> wrote: > Thank you, that's interesting. So all such numbers are divisible by 9. I > didn't think about it. > > You might be interested in my related question: > > https://math.stackexchange.com/questions/4348279/what-is-the-highest-number-of-digits-so-that-this-number-of-digits-in-a-specific > > From checking about the first 50,000 powers of 2, I didn't find c more > than 5, who actually appears only twice (c is the number of digits who > appear exactly 10% of the time in the decimal form of a specific power of > 2). > > אורי > u...@speedy.net > > > On Tue, Jan 4, 2022 at 6:53 AM Daniel Shahaf <d...@daniel.shahaf.name> > wrote: > >> אורי wrote on Tue, 04 Jan 2022 04:07 +00:00: >> > Are there powers of 2 which give exactly 10% of each of the digits 0 to >> 9 (in >> > decimal form)? >> >> No, because then the sum of the digits would be a multiple of nine, so the >> number wouldn't be a power of two. >> >
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