2016: "OEIS Submissions"

[Steve the Pocket]

Rollover caption: SUB[59]: The submission numbers for my accepted OEIS submissions in chronological order

Over on Reddit, it's a running joke that everything you can possibly imagine, and most of the things you can't, have their own subreddits. To the point where the running joke itself has its own subreddit just for posting links to the weirdest ones you've found. My point is, this is the first time I've heard that there's a website dedicated to just cataloguing lists of numbers, and my reaction is simply "of course that's a thing".

[da Doctah]

Oddly, I already knew about OEIS. In fact, I was the one who suggested the entry A133377 to the guy who submitted it.

[Ken_g6]

This got me curious if I could generate 200TB of nines. Well, I think I can:

Code: Select all

perl -e 'for($i=0; $i < 200*1024; $i++) { print "9"x(1024*1024*1024); print STDERR "$i GB so far\n" }'

Then the next question would be how to submit it? Gzip was too big to be practical. So were bzip2 and xz. Oddly, bzip2 did the best, and it's pretty orderly. So I decided to try bzip2 on it again. It works quite well. The main problem is I estimate it would take five days to generate the full 200TB!

Here's a base64 of the first 270,000,000,000 nines, double-bzipped:

Code: Select all

QlpoOTFBWSZTWbyCwBUDJad/9VFgAIBBQGFgMgDIMABgEABAIFQAITAABBQAQAHbklQGGRgTTAmQ
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28YJj4u5IpwoSD6uy94A


[gd1]

2 more comics till we reach 2018 in 2018...

[Millah]

This got me curious if I could generate 200TB of nines. Well, I think I can:

Code: Select all

perl -e 'for($i=0; $i < 200*1024; $i++) { print "9"x(1024*1024*1024); print STDERR "$i GB so far\n" }'

Then the next question would be how to submit it? Gzip was too big to be practical. So were bzip2 and xz. Oddly, bzip2 did the best, and it's pretty orderly. So I decided to try bzip2 on it again. It works quite well. The main problem is I estimate it would take five days to generate the full 200TB!

Here's a base64 of the first 270,000,000,000 nines, double-bzipped:

Code: Select all

QlpoOTFBWSZTWbyCwBUDJad/9VFgAIBBQGFgMgDIMABgEABAIFQAITAABBQAQAHbklQGGRgTTAmQ
xNGBhkYE0wJkMTRgJqqoaaaZMRoGh6mNMgUqqMJpgjIwCYJndApSsIFKV3wKUryhREclVER7KqIj
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28YJj4u5IpwoSD6uy94A


If you zip it, is it still 200TBs of 9s?

[drachefly]

psst… use a run-length encoder first.

[Ken_g6]

If you zip it, is it still 200TBs of 9s?

Hm. If each "9" is a byte, then I think it's still 200TBs of 9s. But maybe not.

270 billion 9s took 5088 bytes. Then, 200TB of double-bzipped 9s would be...about 10 sextillion 9s!

psst… use a run-length encoder first.

I didn't think they could read a run-length encoder's files. I figured maybe they could read bzip2.

As it turns out, they can't. But they'd probably take a Perl program.

[Soupspoon]

https://en.wikipedia.org/wiki/Zip_bomb
https://kottke.org/14/06/the-infinitely-large-zip-file

[Tub]

psst… use a run-length encoder first.

Backreferences are just as good as run-length encoding, the limit here is that common implementations (zip/gzip/deflate etc) have a fixed bit-size for the "length" parameter. For example, a backreference in DEFLATE is at least 24 bits long but has just 8 bits for length. The maximum compression factor is 1:86 = ~1.1%.

bzip2 should produce great results here. The first three steps (initial RLE, burrow-wheeler transform, MTF) are counterproductive in this case, but you still end up with a string with reasonably long runs - an input of ~43MB will end up as 5 different runs instead of just one.
The following RLE has no limit on the run length, except the block size. Including block headers, the end result should be a compression ratio about 1:1.000.000, but on 200TB that's still 200MB. (As Ken has already figured out, the blocks do repeat, so compress recursively.)

/edit: actually, screw RLE. All you need is a good entropy coder, because the entropy of 200 trillion '9's followed by 'eof' is just around ~49 bit, plus header.

[GlassHouses]

Over on Reddit, it's a running joke that everything you can possibly imagine, and most of the things you can't, have their own subreddits. To the point where the running joke itself has its own subreddit just for posting links to the weirdest ones you've found. My point is, this is the first time I've heard that there's a website dedicated to just cataloguing lists of numbers, and my reaction is simply "of course that's a thing".

The OEIS existed before Reddit made this kind of thing cool, though. According to the OEIS web site, it was founded in 1964... Although I have trouble reconciling that date with the "On-Line" part of OEIS, since that's five years before ARPANET.

[madaco]

OEIS is useful and good

[Farabor]

The OEIS existed before Reddit made this kind of thing cool, though. According to the OEIS web site, it was founded in 1964... Although I have trouble reconciling that date with the "On-Line" part of OEIS, since that's five years before ARPANET.

If you dig a bit deeper, you'll find it was originally just the EIS, kept on paper. I've used it in the past in my course on analytic combinatorics.

[Yerushalmi]

One of the sequences was approved: https://oeis.org/A316599

[speising]

One of the sequences was approved: https://oeis.org/A316599

and when reading the description, we now know why randall's submissions get rejected: not because they're dumb, but because they're not precisely enough defined.

[Yerushalmi]

It wasn't rejected, it was... workshopped.

[cellocgw]

This got me curious if I could generate 200TB of nines. Well, I think I can:

Code: Select all

perl -e 'for($i=0; $i < 200*1024; $i++) { print "9"x(1024*1024*1024); print STDERR "$i GB so far\n" }'

Then the next question would be how to submit it? Gzip was too big to be practical. So were bzip2 and xz. Oddly, bzip2 did the best, and it's pretty orderly. So I decided to try bzip2 on it again. It works quite well. The main problem is I estimate it would take five days to generate the full 200TB!

Here's a base64 of the first 270,000,000,000 nines, double-bzipped:
{code snipped}

Best clickbait of the month. I fear for the future of mankind if anyone tries to unzip that string.

Strangely enough, I can zip 200TB of "9" into a rather smaller file. Another case of progress causing regression (where 'progress' is defined as 'useless status message' )


Also:
I knew about OEIS already. Plus I'm an OTTer. They were right when they called me a nerd.

[orthogon]

One of the sequences was approved: https://oeis.org/A316599

and when reading the description, we now know why randall's submissions get rejected: not because they're dumb, but because they're not precisely enough defined.

Loving how one of the key details is related to keming.

[GlassHouses]

Gzip was too big to be practical. So were bzip2 and xz.

Strangely enough, I can zip 200TB of "9" into a rather smaller file.

How? Don't zip and gzip use the same compression algorithm?

[cellocgw]

Gzip was too big to be practical. So were bzip2 and xz.

Strangely enough, I can zip 200TB of "9" into a rather smaller file.

How? Don't zip and gzip use the same compression algorithm?

I dunno, but I do know duplicate replies occasionally sneak into threads.

[cellocgw]

Gzip was too big to be practical. So were bzip2 and xz.

Strangely enough, I can zip 200TB of "9" into a rather smaller file.

How? Don't zip and gzip use the same compression algorithm?

But if I don't include all the comment strings, I have nothing but '9's, a zero-information file. RLE will return 2 numbers, Nice and small

[grkvlt]

So I decided to try bzip2 on it again. It works quite well.

Surely this shouldn't happen? It would mean bzip2 isn't a very good compression algorithm, since the entropy of its output should be maximised and therefore uncompressible?

EDIT: Oh, there are repeated blocks in the output, so recursive compression will make it smaller, right. Still, I wonder why the algorithm doesn't handle this itself, and repeatedly apply until no reduction is found, and prepend the number of decompression steps as an extra byte at the beginning, normally 0x01.

[Archgeek]

This got me curious if I could generate 200TB of nines. Well, I think I can:

Code: Select all

perl -e 'for($i=0; $i < 200*1024; $i++) { print "9"x(1024*1024*1024); print STDERR "$i GB so far\n" }'

Then the next question would be how to submit it? Gzip was too big to be practical. So were bzip2 and xz. Oddly, bzip2 did the best, and it's pretty orderly. So I decided to try bzip2 on it again. It works quite well. The main problem is I estimate it would take five days to generate the full 200TB!

Here's a base64 of the first 270,000,000,000 nines, double-bzipped:

Code: Select all

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SviBSlYkFKVigkRwlURH8qoiNqqiIz/UqiI6yqIjbKoiOFBSlfcClK/YFKV/wCI5qqIjoqoiPEqi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If you zip it, is it still 200TBs of 9s?

Truly a Zen koan for our time.

[ucim]

Still, I wonder why the algorithm doesn't handle this itself, and repeatedly apply until no reduction is found, and prepend the number of decompression steps as an extra byte at the beginning, normally 0x01.

Perhaps because there's not much call for 200TB of 9s, and the added complexity isn't worth the added benefit?

Jose

[keldor]

Still, I wonder why the algorithm doesn't handle this itself, and repeatedly apply until no reduction is found, and prepend the number of decompression steps as an extra byte at the beginning, normally 0x01.

Perhaps because there's not much call for 200TB of 9s, and the added complexity isn't worth the added benefit?

Jose

Some file compression algorithms do this. This has led to malicious files that recursively decompress to "data" petabytes in size, or worse, carefully constructed files that decompress back into themselves infinitely.

https://en.m.wikipedia.org/wiki/Zip_bomb

[Steve the Pocket]

One of the sequences was approved: https://oeis.org/A316599

Being the sort of oddball that I am, I can't help but be amused that they changed it to Arial because Helvetica is "proprietary". Do they think Arial is in the public domain or something? 'Cuz it ain't.

[Yerushalmi]

One of the sequences was approved: https://oeis.org/A316599

Being the sort of oddball that I am, I can't help but be amused that they changed it to Arial because Helvetica is "proprietary". Do they think Arial is in the public domain or something? 'Cuz it ain't.

An objection that was raised immediately on the OEIS mailing list I haven't checked if it's been resolved.

[SuicideJunkie]

An objection that was raised immediately on the OEIS mailing list I haven't checked if it's been resolved.

I really hope there is an online archive where we can read this assuredly amusing exchange, and that someone will link to it.

[pernishus]

Thread activity: let's post sequences that we think are interesting and possibly obscure
I'll start.
http://oeis.org/A084398
Definition: Except for a(1) = 1, rearrangement of natural numbers such that a(n) is not equal to n, but the prime signature of a(n) is the same as that of n.

Initial 20 terms:
1, 3, 2, 9, 7, 10, 5, 27, 4, 6, 13, 18, 11, 15, 14, 81, 19, 12, 17, 28

[yae9911]

An objection that was raised immediately on the OEIS mailing list I haven't checked if it's been resolved.

I really hope there is an online archive where we can read this assuredly amusing exchange, and that someone will link to it.

Unfortunately the archiving process of the SeqFan mailing list is currently broken. At the moment only a single post related to the topic is accessible: http://list.seqfan.eu/pipermail/seqfan/ ... 18694.html
Her is a copy of what I have posted to the list in reply to the "proprietary" remark:

The intent of the comment "Helvetica is a proprietary font ...." was different. 99.9xx % of the standard system and program installations on Windows, Linux and perhaps also Mac computers don't provide Helvetica as an option for printing. To get access to Helvetica, one has to buy a license from the Linotype-Hell AG. Most Windows users believe that Arial would deliver "somehow" similar results to Helvetica, but they cannot verify this assumption. The same caveat applies to all other substitutions for Helvetica in Ghostscript, Open/Libre office, ...
The only way for myself to use genuine Helvetica would be to write a Postscript file, re-activate my first PC and send the file to the legacy HP LaserJet 4ML postscript printer that has an authorized built-in capability to interpret Helvetica correctly.

Even the expensive Adobe CS tools like Illustrator, InDesign, etc. didn't include the Helvetica font in the standard installation. Arial was available, an I'll use InDesign and its pdf export to create the announced graphical example. So the task described in the comic " .... printed in Helvetica" is only solvable for graphics professionals with access to a licensed copy of the font.

In contrast, all Windows installations -still- include the Arial True Type font defined in the file
arial.ttf, size 1036584, dated 2018 Apr 12 01:34, last distributed with Windows 10 Pro Version 1803. What I did, was to extract the Adobe Font Metrics information from this file into an .afm file using
https://www.files-conversion.com/font-converter.php
which seems to use FontForge https://fontforge.github.io/en-US/ for the conversion. I don't think that there is anything violating license rules with this procedure.

In the meantime I have found an "official" information on the font metrics of Helvetica at Adobe's Font technical notes webpage https://www.adobe.com/devnet/font.html. It provides a link to
http://download.macromedia.com/pub/deve ... 4_AFMs.zip , which includes helvetica.afm. From its content, it seems that "integers... printed in Helvetica" would produce massive differences to "printed in Arial", due to the absence of the kern pair definition "KPX one one -74" found in arial.afm, but not in helvetica.afm, that causes the shrinking of print width for numbers containing consecutive ones. To be provocative, one can say "Arial intentionally messes up the printing of numbers".
See the second (Earl Jenkins's) answer in https://stackoverflow.com/questions/394 ... ost-pixels and David Harralson's answer in https://www.quora.com/Why-did-Microsoft ... to-Calibri for some historical background.

In the meantime A316600 is available:
http://oeis.org/A316600

[drachefly]

psst… use a run-length encoder first.

Backreferences are just as good as run-length encoding, the limit here is that common implementations (zip/gzip/deflate etc) have a fixed bit-size for the "length" parameter. For example, a backreference in DEFLATE is at least 24 bits long but has just 8 bits for length. The maximum compression factor is 1:86 = ~1.1%.

bzip2 should produce great results here. The first three steps (initial RLE, burrow-wheeler transform, MTF) are counterproductive in this case, but you still end up with a string with reasonably long runs - an input of ~43MB will end up as 5 different runs instead of just one.
The following RLE has no limit on the run length, except the block size. Including block headers, the end result should be a compression ratio about 1:1.000.000, but on 200TB that's still 200MB. (As Ken has already figured out, the blocks do repeat, so compress recursively.)

/edit: actually, screw RLE. All you need is a good entropy coder, because the entropy of 200 trillion '9's followed by 'eof' is just around ~49 bit, plus header.

Entropy coders need implementations. If Bzip2 starts with an RLE and doesn't just completely finish right there, then they didn't design it with super-huge runs in mind.

Also, you're supposed to put the BWT before your RLE. Why RLE first?

[Tub]

Also, you're supposed to put the BWT before your RLE. Why RLE first?

bzip has two RLE steps.
RLE -> BTW -> MTF -> RLE
Both RLEs have different encodings and maximum run lengths. The first one is supposed to guard against worst-case inputs; due to its inefficient (but fast) encoding it will actually enlargen most inputs. IIRC the author has since claimed that including it was a mistake.

[Eianz]

But what if the zip bomb is sitting inside compression files and unleash the curse