Fun with powers of 2

[Michael Shiloh]

‪On Tue, Jan 4, 2022 at 10:20 AM ‫אורי‬‎ <uri at speedy.net> wrote:‬

> I apologize about the subject. Feel free to change it. The main post was
> about almost crashing my computer with the command  _py -c
> "print(2**64**3)".
> אורי
> uri at speedy.net
>
>
> On Tue, Jan 4, 2022 at 8:01 AM Michael Shiloh <michaelshiloh1010 at gmail.com>
> wrote:
>
>> Interesting discussion, but the subject seems quite wrong.
>>
>> ‪On Tue, Jan 4, 2022 at 9:32 AM ‫אורי‬‎ <uri at speedy.net> wrote:‬
>>
>>> From checking also powers of 3, I can't find more than c==5 (for 3**20
>>> and 3**124).
>>>
>>> אורי
>>> uri at speedy.net
>>>
>>>
>>> ‪On Tue, Jan 4, 2022 at 7:24 AM ‫אורי‬‎ <uri at 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
>>>> uri at speedy.net
>>>>
>>>>
>>>> On Tue, Jan 4, 2022 at 6:53 AM Daniel Shahaf <d.s at 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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>>
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