A Number Sequence with Everything - Numberphile

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Neil Sloane discusses The Inventory Sequence... See also Jane Street's special page: www.janestreet.com/numberphil...
More links & stuff in full description below ↓↓↓
Neil Sloane is founder of the legendary OEIS: oeis.org/
Inventory Sequence at: oeis.org/A342585
Jane Street's page mentioned in this video at: www.janestreet.com/numberphil... (episode sponsor)
Numberphile is supported by the Simons Laufer Mathematical Sciences Institute (formerly MSRI): bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. www.simonsfoundation.org/outr...
And support from The Akamai Foundation - dedicated to encouraging the next generation of technology innovators and equitable access to STEM education - www.akamai.com/company/corpor...
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Subscribe: bit.ly/Numberphile_Sub
Video by Brady Haran and Pete McPartlan
Shout-out to eagle-eyed Michael Colognori who helped with checking.
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Brady's videos subreddit: / bradyharan
Brady's latest videos across all channels: www.bradyharanblog.com/
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9 ноя 2022

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Комментарии : 441

@numberphile Год назад

Check out Jane Street's sidewalk sequence at: www.janestreet.com/numberphile2022 Visit the OEIS at: oeis.org/

@FebruaryHas30Days Год назад

First reply I use OEIS

@paulthompson9668 Год назад

4:53 The envelope reminds me of the Fibonacci numbers, which has a cosine in it.

@Ethan-lu7gd Год назад

OEIS is one of my favourite websites, It's always a joy to see videos on the myriads of wonderful sequences it contains! Thank you!

@maitland1007 Год назад

The Jane St thing sounds to me like "Hey, if you are smart and like math, come help us make rich people even richer". Am I wrong?

@paulthompson9668 Год назад

@@maitland1007 It sounds like a cult.

@rozhenko Год назад

Honored to be mentioned in this video by the great Neil Sloane! Thank you Neil and thank you Numberphile for posting the video.

@iamthecondor Год назад

To be fair, you've earned it 😅

@danielg9275 Год назад

Awesome when a celebrity reacts to the video!

@staizer Год назад

What is this sequence like in binary?

@jonaslarsson5279 Год назад

@@staizer It's not based on the digits but on the numbers. I.e. when 10 shows up you don't view it as a one and a zero, but as a ten. Interesting question nonetheless, were you to interpret a 10 as a one and a zero.

@archivist17 Год назад

Thanks for a creative and beautiful sequence, Joseph!

@nicksamek12 Год назад

A beautiful message to end the video with. A lot of math isn't in the destination, but the understanding you develop on the journey.

@lonestarr1490 Год назад

So you gonna tell me, maybe the real math is the friends we made along the way?

@quintrankid8045 Год назад

Shouldn't we generalize that?

@jomolisious Год назад

Journey before Destination.

@JorgetePanete Год назад

A 2000 theorems journey starts with 1 statement

@angelodc1652 Год назад

@@lonestarr1490 I was about to say something similar

@Drej9 Год назад

Neil Sloane is an international treasure. With every video he appears in, the content becomes so interesting and engaging. More Neil!

@Triantalex 5 месяцев назад

@julesmcbride2692 Год назад

"We have the variations, but we don't know what the theme is." What a stellar analogy for mathematical puzzles.

@aceman0000099 Год назад

The music was like someone getting chased, and stumbling, but every time they stumble they manage to run a bit further and the suspense builds

@vigilantcosmicpenguin8721 Год назад

@@aceman0000099 It's a neat effect how the tempo doesn't change, yet it feels like something is getting away from you.

@matthewdodd1262 Год назад

Strangley, even the fun maths is super important. When people find new and weird ways of doing something silly and fun with stuff like this, it can bring forward new ideas which can be used to solve more important problems in mats

@Axacqk Год назад

On a meta-level, it is not that surprising that a sequence defined recursively in terms of _all_ its previous values exhibits interesting behavior. No information is ever lost - every element of the sequence will be used infinitely often in computing subsequent elements. The sequence just meditates upon itself forever, without ever losing any "insight" once gained.

@AlexBaklanov Год назад

This man loves what he's doing. He looks so satisfied at the end of the video )

@DiamondzFinder_ Год назад

I was literally just rewatching the planing sequence video when I got this notification.... This guy is so satisfying to listen to, and the sequences he shows us are so fun! Love it

@DekarNL Год назад

Totally agree. Would love to see progress made into understanding these types of sequences.

@maynardtrendle820 Год назад

Look up the 'Experimental Mathematics' RU-vid channel, and you'll find some Zoom lectures from Neil regarding all kinds of OEIS sequences. Also, a lot of other cool videos! It's a small channel from Rutgers University, but Neil is a constant on it.

@Triantalex 5 месяцев назад

@DiamondzFinder_ 5 месяцев назад

Thanks for the recommendation! @@maynardtrendle820

@DekarNL Год назад

Love Neil and the OEIS. Used it for a math puzzle the other day :)

@MushookieMan Год назад

That's cheating

@teemuaho4807 Год назад

I often think about math instead of actually concentrating on whatever lesson is at hand and whenever i figure out a cool sequence or constant i plug it in the OEIS to see if there's any cool formulae or connections with other numbers

@Triantalex 5 месяцев назад

@JaxonHaze Год назад

I love this guy he has the most calming voice

@dit-zy Год назад

Neil is so excitedly passionate and I just absolutely love it! He's adorable and so interesting to hear from 💕

@2Cerealbox Год назад

Two great quotes from this video. "Here, we have the variations. But we don't know the theme." "Maybe in itself its just a sequence. But who knows where it will lead."

@kikivoorburg Год назад

Neil is awesome, his excitement is super contagious!

@fleabag500 Год назад

neil's videos are some of my absolute favourites. he has an amazing, relaxing voice.

@Xamimus Год назад

Neil Sloane is one of the best Numberphile presenters!

@gandolph999 Год назад

Your enthusiasm and fascination with this Inventory Sequence are pleasantly infectious. It is interesting.

@altejoh Год назад

I'd be really curious to see a Fourier Transform of this series, it reminds me a lot of energy levels and spectra from chemistry/physics.

@aceman0000099 Год назад

I don't know if it's possible

@robertr7923 Год назад

Me too! Should be doable in a program. You can find the sequence on the OEIS

@bur2000 Год назад

@@aceman0000099 You'd have to interpolate the original sequence to get a continuous function, I think. Fourier transformation of discreet values doesn't make sense - unless I'm mistaken.

@marclink0 Год назад

@@bur2000 as far as I know, both Discrete Fourier Transform and Continuous Fourier Transform exist

@DonCamilloArte Месяц назад

It's one of my favorite posts in numberphile - thanks for that!

@numberphile Месяц назад

glad you liked it.

@randy7894 Год назад

Neil is a math poet. I love his video's.

@AngeloEduardo-gs6yv 10 месяцев назад

Kkkk😊

@Bethos1247-Arne Год назад

Every video with this guy is a must-watch.

@thehearth8773 Год назад

I can't help but notice, there's also the little digits Neil draws to say which number each term refers to. I wonder how the sequence would change if you included those! It'd be kind of like the look-and-say sequence, but without grouping the numbers.

@applechocolate4U Год назад

This is without a doubt my favorite numberphile video

@AbandonedMines11 Год назад

This was all so very fascinating. I’m a pianist, too, and found the musical tie-in to be very intriguing.

@j.thomas1420 Год назад

Boulez would certainly have liked to make something from this. The closest piece for piano I know to that sequence is Ligeti, Devil Staircase.

@marvinabarquez8915 Год назад

I see you went down the YT alg rabbit hole too

@txikitofandango Год назад

It's never a bad time to thank Neil Sloane for his contributions which have helped mathematicians around the world for generations.

@MichaelGrantPhD Год назад

If I were a greedy inventory taker, I wouldn't re-start my inventory when I get a zero. Instead, I would immediately jump to the number corresponding to the count I just arrived at. For example, if I'm currently counting the number of 8's, and I count 3 of them, I would count the number of 3's next. Of course I know that will be one more than the last time I counted it. So I never really have to re-count anything, I'm just incrementing by one every time.

@derekhasabrain Год назад

I show up to every video with Neil Sloane and I always will!

@TranscendentBen Год назад

8:54 He mentions John Conway - it was just after the first minute that I thought of the look-and-say sequence that Conway had analyzed and apparently made famous. My goodness I should have been a mathematician! I could sit around, drink coffee and come up with sequences like this all day! ;-)

@mathphysicsnerd Год назад

Always love to see a Sloane video, the man makes my day

@LMacNeill Год назад

I could listen to him talk for hours. Always interesting and engaging -- I've watched every video you've made with him. I do hope you'll have more videos with him in the future.

@thomaschevrierlaliberte5884 Год назад

Those rows of book on the shelf facing him seem like such a lifetime of mathematical passion.

@simonblake1434 Год назад

Love a Neil Sloane video - thank you Numberphile :)

@ComboClass Год назад

The OEIS is an amazing resource. One of the best websites in existence

@Mechanikatt Год назад

Oh boy, more Neil!

@EvilSandwich Год назад

After I listen to this absolutely fascinating discussion, I have come to the conclusion that, for humanity, mathematicians are quite possibly one of the most important and vital community of completely batshit crazy people in the world.

@mairsilpretner6119 Год назад

Neil is always an amazing guest, his love for these sequences is very infectuous

@FloydMaxwell Год назад

Great background music for a suspense scene

@jhoylangoncalves3127 Год назад

I just love this gentleman, his passion about numbers and sequences are just intoxicated

@FlintStryker 4 месяца назад

Always enjoy his videos. What truly amazes me though is there was a time when he consciously chose that wallpaper. 😂

@SpooNFoy Год назад

The worst Neil Sloane video I've ever watched was excellent. Can never have too much of this man.

@YG-ub4dk Год назад

Always love the Neil Sloane sequences videos :)

@Hamuel Год назад

I adore seeing Neil explain more sequences!

@davidmurvai40 Месяц назад

The content is amazing but his speaking voice is absolutely wonderful ❤. So soothing and such a captivating style.

@SuperYoonHo Год назад

I love vids with Neil Sloane!!!😍

@reidflemingworldstoughestm1394 Год назад

Love the Sloane videos.

@thebrewster Год назад

"it's very irregular, and wonderful" love the enthusiasm, new to this channel.

@I_Was_Named_This_Way... Год назад

I made something for this in Excel, took about an hour to make but it works flawlessly

@carltonleboss Год назад

Love a Neil sequence video

@Reggiamoto Год назад

Videos with Neil Sloane are always a highlight. One question I have is whether every number will appear? Isn't it possible that one number gets skipped by all previous numbers, so you'd always have to take inventory for the same number from that point?

@christianellegaard7120 Год назад

No, I don't think so. The zeros take care of that. Every time you take inventory there is one more zero. So all the numbers appear in the first column.

@mellowyellow7523 Год назад

rewatch around 2:30 he says the next line will always be the next number

@Boink97 Год назад

Apart from the trivial appearance (when the numbers appear because of the zeros) - do we know if every numbers appears at least once more?

@jimmyh2137 Год назад

@@Boink97 that's a great question, we need answers!

@SgtSupaman Год назад

@@Boink97 , due to the fact that numbers are constantly being added and never taken away, this doesn't seem as though it would ever skip any number infinitely, even if you don't count the number's required initial appearance. We can see that the amount of each number (the columns formed in the way he lays it out) will continue to increase. They may not increase on every row, but they all increase. So, once a number gets a 1 in its column (which it has to, given the "trivial appearance"), it will certainly increase from there.

@yetismacker7053 Год назад

thank you Neil!

@jimmyh2137 Год назад

I would love to look at the same sequence with a variation where you also count the "index". So it would go: 0_0 (zero "zeroes") 2_0; (two "zeroes" because you got the "index") 0_1; 4_0; 1_1; 1_2; 0_3; 6_0; 4_1; 2_2; 1_3; 2_4; 0_5; 8_0; 6_1; 5_2; 2_3; 3_4; 2_5; 2_6; 0_7; ... First entry is always 2n (you always have one index for 0 and the last entry) but the pattern for other digits looks very different, or maybe we can find some connection with the "base" sequence!

@SgtSupaman Год назад

I thought at first that is how the pattern would work in the video, since he wrote those subscripts and asked how many we could see, but apparently, they were just there to help him explain/keep track of the meaning of each digit. The sequence in the video could be written without the subscripts entirely (and in one continuous line). An interesting aspect of doing it in a way that includes the index is that you are guaranteed that the numbers in the columns will always increase by at least one for every additional row, because the index is will always be present in each row. By the way, slight error in your index-counting sequence. The 4th line should have "2_4;" instead of "1_4;" (there is a 4 in line three and a 4 earlier in line four), which would change your 5th line to 8_0; 6_1; 5_2; 2_3; 3_4; 2_5; 2_6; 0_7; So far, this suggests each row will stop (by hitting a 0) at 2n-1.

@jimmyh2137 Год назад

@@SgtSupaman Oh yeah, fixed now.

Год назад

I wonder how it changes in different base numbers

@WarriorOfJustice7 Год назад

I love your videos!❤

@guillaumelagueyte1019 Год назад

After seeing the underlying mathematics of the look-and-say sequence, I most certainly hope we will be able to find and explain since structure with this one as well. What an absolute beauty

@Xonatron Год назад

Love this sequence!

@sperenity5883 8 месяцев назад

God bless you, man.

@Algoritmarte Год назад

Awesome sequence and wonderful explanation!

@Doktor_Vem Год назад

Yay more Neil! :D

@shanehebert396 Год назад

Everybody needs someone who talks about them like Dr. Sloane talks about sequences.

@bgtyhnmju7 Год назад

Neil Sloane - what a lovely fellow. Great video.

@mxxtmxnxght Год назад

The plot looks like a banger 808 sample 👀 Need to check it asap!

@JC-zw9vs Год назад

More Neil please.

@archivist17 Год назад

Mesmerising sequence!

@user255 Год назад

I really like his videos! More!

@JacobCanote Год назад

The patterns are beautiful.

@theemptyatom Год назад

his chuckle is Epic

@shade4835 Год назад

I love this one so much

@zoeg5304 Год назад

So cool!

@arekkrolak6320 Год назад

Very interesting material, I wish to see some more youtube material around this topic!

@tx2016 Год назад

Love this stuff

@devjock Год назад

The sequence looking for a killer app. Quite distinctly put, Mr Sloane!

@Pfhorrest Год назад

Even before the big obvious leap in the curve that you called attention to, I was already noticing a smaller leap in the earlier part of the curve, and now looking at the larger curve with the big obvious leaps in it there are even more clearly a series of ever-smaller leaps near the beginning of the sequence too.

@sambolt8659 Год назад

I loved this video so much

@numberphile Год назад

Great!

@LluviaSelenita Год назад

I love these pieces of math art. I was hoping this would go towards music. It's awesome.

@inrlyehheisdreaming Год назад

Regardless of the inherent value of the sequences themselves, the best of these videos is seeing how happy they make him!

@hosz5499 Год назад

A Great game for elementary students, to build concepts of sequence, logic, infinity, graph, etc etc!! I will do this in my next math lecture

@alexthebold Год назад

Oh, this guy is great!

@somebody2988 Год назад

I adore all of his video. He really makes math interesting, captivating and fun! I already dread for the day he shall pass.

@davidvegabravo1579 Год назад

I know nothing about math, but i love this guy!

@dewaard3301 Год назад

The way Neil eases us into his sequences makes me certain he's got grandkids that he loves to read to.

@mikeness5074 Год назад

This guy is really the OG of calculation!!!!

@davidbrooks2375 Год назад

The more we see of Neil's office, the cooler it gets!

@swankitydankity297 Год назад

Very cool sequence!

@Phriedah Год назад

I can't be the only one who thought that the music felt really ominous in a cool way. Like, if I wanted background music for a haunted house, just play the first 10,000 terms in the series on loop over a speaker.

@christopherhinzman7424 Год назад

Please do a video on the infinite sidewalk!! That’s fascinating. Thanks for sharing the link!

@senthilkumaran5255 Год назад

Is this somehow connected to the Mandelbrot set? That's what struck me when I saw "this sequence has everything" and the fundamental unpredictable yet beautiful nature of it seems very similar to Mandelbrot. The fact that when converted to music, it seems to follow a pattern of highs to lows with slight variatons for each block/chunk is like penrose/fractal tiling that repeats infinitely with small variations, aperiodic yet beautiful!

@connorohiggins8000 Год назад

I really enjoy the OEIS videos. I got a sequence accepted a few years ago (A328225) after one of these videos. This just reminded me that I never figured out why my sequence looked the way it did when it was plotted. I would love to hear some thoughts. I am not a mathematician in any form, so it could be absolutely nothing.

@dallangoldblatt7368 Год назад

I'm gonna look, I'll get back to you in a bit

@LunizIsGlacey Год назад

Oh wow, that's quite cool! Seems like such a strange rule, but the plot is very interesting!

@connorohiggins8000 Год назад

@@dallangoldblatt7368 Thanks Dallan

@kindlin Год назад

@@connorohiggins8000 What does prime(n) mean? Checking to see if it's prime? Does it return 1 or 0? But then, what would prime(prime(n)) be? How does that sequence work? (This is just a formula question, I simply do not know what prime(n) might return.)

@connorohiggins8000 Год назад

@@kindlin Hi, so prime(n) means the nth prime, prime(1) = 2, prime(2) = 3, prime(3) = 5 .... If n = 2 then prime(prime(n)) = prime(3) = 5. It is a bit of a weird sequence.

@TAP7a Год назад

Stockhausen and Xenakis would be very proud of Sloane’s “Variations con Théme Perdu”

@mrwizardalien Год назад

I didn't know you could download those as MIDI! I immediately went off to go make some sequence music!

@C0rnyFlak3s Год назад

More please!

@thelocalsage Год назад

i got very excited about this and was playing with it, started one where i did inventory but inventoried numbers greater than or equal to the index (later found it in OEIS already) but i found some fun patterns and would love to know why they’re like that! there was a fractal pattern that emerged and also there was another OEIS sequence correlated with the peaks. would love to hear someone like Neil explain why

@hindigente Год назад

It's impossible not to chuckle at ~5:00 when Sloane shows the sequence's unexpected behaviour.

@andybaldman Год назад

Why?

@rayscotchcoulton Год назад

I love his reply to Brady's comment at that point when he says it's irregular... and wonderful. The way he says that makes me smile.

@hindigente Год назад

@@andybaldman Because of both how unpredictable the sequence's envelope turns out to be and how endearingly Neil Sloane presents it.

@vigilantcosmicpenguin8721 Год назад

Just when you thought things were making sense.

@Tarrandus Год назад

Always gonna celebrate each new Neil Sloane video, 🎉 and always gonna ask for more ❤

@TeacherNaseebZada Год назад

Its very helpful

@patcheskipp Год назад

It kind of sounds like the roar of a crowd that is in a panic. It gets excited and then the voices come to a murmur and then gets excited again. Or possibly a paniced or anxious mind

@10-year-oldcalculus19 7 месяцев назад

5:37 Aight gotta set THIS to be my ringtone

@clueless3773 Год назад

This video is interesting!

@thewatermelon3831 Год назад

I'm new to this, and i have a few questions if anyone may be so kind to answer: 1. What is the point of the sequence? 2. Why use a marker over paper? 3. What was so extraordinary about the music?

@PhngluiMglwnafh Год назад

I see a Neil Sloane video, I watch it, no questions asked

@mrmorganmusic 6 месяцев назад

Love this interview. One small note (ha): I wish his musical example had been Bach’s Goldberg Variations, which are themselves loaded with very purposeful mathematical design elements. Still, I appreciate a musical reference very much!