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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