Fun with powers of 2
On Tue, Jan 4, 2022 at 10:20 AM אורי 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 > u...@speedy.net > > > On Tue, Jan 4, 2022 at 8:01 AM Michael Shiloh > wrote: > >> Interesting discussion, but the subject seems quite wrong. >> >> On Tue, Jan 4, 2022 at 9:32 AM אורי wrote: >> >>> 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 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 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. > ___ >>> Linux-il mailing list >>> Linux-il@cs.huji.ac.il >>> http://mailman.cs.huji.ac.il/mailman/listinfo/linux-il >>> >> ___ Linux-il mailing list Linux-il@cs.huji.ac.il http://mailman.cs.huji.ac.il/mailman/listinfo/linux-il
Re: Python on Ubuntu 18.04.6 LTS
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 u...@speedy.net On Tue, Jan 4, 2022 at 8:01 AM Michael Shiloh wrote: > Interesting discussion, but the subject seems quite wrong. > > On Tue, Jan 4, 2022 at 9:32 AM אורי wrote: > >> 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 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 >>> 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. >>> ___ >> Linux-il mailing list >> Linux-il@cs.huji.ac.il >> http://mailman.cs.huji.ac.il/mailman/listinfo/linux-il >> > ___ Linux-il mailing list Linux-il@cs.huji.ac.il http://mailman.cs.huji.ac.il/mailman/listinfo/linux-il
Re: Python on Ubuntu 18.04.6 LTS
Interesting discussion, but the subject seems quite wrong. On Tue, Jan 4, 2022 at 9:32 AM אורי wrote: > 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 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 >> 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. >>> >> ___ > Linux-il mailing list > Linux-il@cs.huji.ac.il > http://mailman.cs.huji.ac.il/mailman/listinfo/linux-il > ___ Linux-il mailing list Linux-il@cs.huji.ac.il http://mailman.cs.huji.ac.il/mailman/listinfo/linux-il
Re: Python on Ubuntu 18.04.6 LTS
>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 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 > 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. >> > ___ Linux-il mailing list Linux-il@cs.huji.ac.il http://mailman.cs.huji.ac.il/mailman/listinfo/linux-il
Re: Python on Ubuntu 18.04.6 LTS
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 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. > ___ Linux-il mailing list Linux-il@cs.huji.ac.il http://mailman.cs.huji.ac.il/mailman/listinfo/linux-il
Re: Python on Ubuntu 18.04.6 LTS
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. ___ Linux-il mailing list Linux-il@cs.huji.ac.il http://mailman.cs.huji.ac.il/mailman/listinfo/linux-il
Re: Python on Ubuntu 18.04.6 LTS
NOT an answer to your question, but instead of a link to python3.8, I added 2 lines to .bash_aliases: alias p="python3.8" alias p2="python2.7" On Tue, 4 Jan 2022 06:07:43 +0200 אורי wrote: > Hi, > > /usr/bin/python is defined on my server as a link to the > deprecated python2.7, and I didn't want to break anything, so I > defined /usr/bin/_py as a link to python3.8. I wanted to check how > many bytes a giga and tera is, so I ran _py -c "print(1024**3)" and > _py -c "print(1024**4)". Then I checked _py -c "print(2**64)" and I > wanted to check _py -c "print(2**64**3)", which I thought will be > equal to _py -c "print(2**192)" (_py -c "print((2**64)**3)"), but no > - this gave me a number with 78914 digits and I'm glad it didn't > crash my server (4 or 5 or 6 would have crashed it). Since when > 2**64**3 is 2**(64**3) and not (2**64)**3? Anyway I also checked > 2**10**6 (==2**100) and I found out that it contains exactly 10% > digits of 6, and I even created a small program to calculate the > powers of 2 that give exactly 10% digits of 6. Are there powers of 2 > which give exactly 10% of each of the digits 0 to 9 (in decimal form)? > > for n in range(1, 10 ** 6 + 1): > a = 2 ** n > b = list(str(a)) > s = sum([1 if i == "6" else 0 for i in b]) > if (s * 10 == len(b)): > print(n, len(b), s) > > Thanks, > > אורי > u...@speedy.net -- Shlomo Solomon http://the-solomons.net Claws Mail 3.17.5 - KDE Plasma 5.18.5 - Kubuntu 20.04 ___ Linux-il mailing list Linux-il@cs.huji.ac.il http://mailman.cs.huji.ac.il/mailman/listinfo/linux-il
Python on Ubuntu 18.04.6 LTS
Hi, /usr/bin/python is defined on my server as a link to the deprecated python2.7, and I didn't want to break anything, so I defined /usr/bin/_py as a link to python3.8. I wanted to check how many bytes a giga and tera is, so I ran _py -c "print(1024**3)" and _py -c "print(1024**4)". Then I checked _py -c "print(2**64)" and I wanted to check _py -c "print(2**64**3)", which I thought will be equal to _py -c "print(2**192)" (_py -c "print((2**64)**3)"), but no - this gave me a number with 78914 digits and I'm glad it didn't crash my server (4 or 5 or 6 would have crashed it). Since when 2**64**3 is 2**(64**3) and not (2**64)**3? Anyway I also checked 2**10**6 (==2**100) and I found out that it contains exactly 10% digits of 6, and I even created a small program to calculate the powers of 2 that give exactly 10% digits of 6. Are there powers of 2 which give exactly 10% of each of the digits 0 to 9 (in decimal form)? for n in range(1, 10 ** 6 + 1): a = 2 ** n b = list(str(a)) s = sum([1 if i == "6" else 0 for i in b]) if (s * 10 == len(b)): print(n, len(b), s) Thanks, אורי u...@speedy.net ___ Linux-il mailing list Linux-il@cs.huji.ac.il http://mailman.cs.huji.ac.il/mailman/listinfo/linux-il
