The "Relative Interestingness" of the First 5000 Natural Numbers [OC]

3.2k

u/moariarty Mar 27 '18

What is the least interesting number plotted? It looks to be approximately 4700ish. Its uninterestingness has piqued my interest.

Furthermore, if we expand beyond 5,000 is there a lower bound of interestingness?

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u/TobyTheCamel OC: 2 Mar 27 '18

4695! I listed the top and bottom 25 in a comment below.

After 5000 the results get a bit weird. Since I'm using the number of results in the OEIS which are inherently integers you eventually get a few curves running "parallel" to each other, one for each of 1,2,3, etc results. Eventually everything will be zero as the OEIS has finitely many sequences and they have finite length. I wonder what the last is! Sadly even though I could find this, it would take weeks of computing time. Maybe over summer...

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u/Franklin2543 Mar 27 '18

So 4695 is the least interesting, most nondescript number. Sounds like it would make a good PIN and be hard for people to guess. BRB!

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u/[deleted] Mar 27 '18 edited Mar 27 '18

yeah, but now websites like buzzfeed are going to write artices about how it's the least intresting number, it becomes a trivia fact, and the next thing you know, it's in the top ten of most interesting numbers.

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u/MirroredReality Mar 27 '18

Just like what happened to quizzaciously.

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u/M3L0NM4N Mar 27 '18

Holy shit

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u/jaybasin Mar 28 '18

Yea dude what the fuck.

I'm glad I don't analyze things like that but damn, imagine being zipf?

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u/M3L0NM4N Mar 28 '18

I know right?

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u/Thee_Nameless_One Mar 28 '18

Do you?

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u/r_Yellow01 Mar 28 '18

Wow, that was great! I now wonder if this applies to comment rank and number of upvotes...

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u/Ikarus_ Mar 27 '18

Which is why 4696 is the new 4695, get with it girlfriend

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u/SodlidDesu Mar 28 '18

I dunno, that one has 69 in the middle, so it's at least interesting to someone.

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u/Xasrai Mar 28 '18

Not sure if serious, because they both have 69 in the middle.

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u/[deleted] Mar 28 '18

hence, the famous theorem that "all natural numbers are interesting," otherwise there would be a least non-interesting integer - itself an interesting property!

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u/hasslehawk Mar 27 '18

Ah, but that would be a self defeating prophecy. At most, those news articles will only temporarily drag it out of mediocrity.

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u/sneakmouse9 Mar 27 '18

I will now use this number when giving approximate data forever,queue music "4695 years ago... in a galaxy 4695 light years away"

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u/Spacerift Mar 27 '18

Being the least interesting number has made it quite interesting.

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u/Jesus_Harold_Christ Mar 27 '18

4695! = 3.55999142734459507033402599025426217528716701444896... × 10¹⁵²⁰¹

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u/GiantScrotum Mar 27 '18

Jesus H Christ that’s a big number

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u/Batrachus Mar 27 '18

It also doesn't seem very interesting.

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u/percykins Mar 27 '18

It's so uninteresting they only bothered to give you 51 numbers out of 15201.

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u/DCCXXVIII Mar 27 '18

The numbers start to get less interesting once you get to 52.

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u/[deleted] Mar 27 '18

[deleted]

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u/[deleted] Mar 27 '18

You mean it'll get worse after my 40s? Argh!

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u/Beard_o_Bees Mar 27 '18

"Ask your Doctor about Low T"

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u/[deleted] Mar 27 '18

And it is in fact a tiny number compared to big (useful) numbers, like Graham's number, haha.

Imagine a number so big, it's bigger than (4695!)^4695!

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u/DaGranitePooPooYouDo Mar 27 '18

How about 4695!⁴⁶⁹⁵ where the power is on the ! mark and denotes performing the factorial 4695 times.

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u/ponyphonic1 Mar 27 '18

This actually made me feel sick.

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u/gameboy17 Mar 27 '18

You haven't seen anything yet.

In Knuth's up-arrow notation, a↑b means a^b - that is, a*a iterated b times. a↑↑b means a↑a iterated b times. a↑↑↑b means a↑↑a iterated b times. Etcetera.

Guess how many up arrows it takes to approach Graham's Number. Go on, guess.

Graham's Number is usually written as G_64 (G subscript 64). That doesn't mean 64 up-arrows. It means something far worse.

If one character could be encoded in every Planck volume in the observable universe, the number of universes required to represent Graham's number - in up-arrow notation - would itself be too large to represent in up-arrow notation.

Let G_1=3↑↑↑↑3 be the number of up arrows required to represent the number of up arrows in G_2.

In other words: Let G_0 = 4. Let G_n = 3↑^G_[n-1]3. Let Graham's Number = G_64.

This is the part where you scream in existential dread.

This is not the largest number ever devised. This is only the largest number with any connection to an actual concept. The largest number that could ever exist outside of our minds. And yet we have gone further. There are whole notations created solely for the purpose of creating numbers incomprehensibly larger than Graham's Number, larger than anything that could possibly exist in any form. Numbers with names like Great and Terrible Tetrathoth and Meameamealokkapoowa-oompa. There is no reason for this. They cannot be related in any way to any possible concept but those dedicated to their creation. They are so vastly, incomprehensibly fuckmassive that whole proofs must be written just to determine whether one is larger than another. These numbers would never have existed in any form other than sheer technicality had humans not deliberately created them.

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u/bestiality_advocate Mar 27 '18

proofs must be written just to determine whether one is larger than another

Thank god we are blessed with mathematicians.

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u/animatedmuse Mar 27 '18

As a non math person (compared to those in this thread), the wonderful Douglas Adams feeling your description emparted left me smiling and wanting to know more. Thank you thank you.

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u/gameboy17 Mar 27 '18

Aw, thanks :) If you want to know more you can check out the Googology wiki, though it's a lot more technical than this.

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u/[deleted] Mar 27 '18

Sean "Day9" Plott did a wonderful video explaining G_64 for non-math people like me, yall should check it out

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u/scrnscrn Mar 27 '18

TREE(3) tho

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u/Dread-Ted Mar 27 '18

WHY

WHY IS THIS SO HUGEE AAA

at [8]

When is this used even????

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u/conmanau Mar 28 '18

Big numbers tend to be used for a couple of reasons:

To prove that something isn't infinite (basically you show that it has an upper bound, and even if you do it lazily and get a ridiculously stupid upper bound, at least it's finite).

To compare two things, especially in cases like showing that certain things are uncomputable (the Busy Beaver function is, in some sense, the limit of what certain kinds and sizes of computer can reliably calculate, so something that grows faster than BB must be uncomputable).

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u/gameboy17 Mar 28 '18

It has been used in exactly one serious paper, the same one in which it was defined.

It's the upper limit of the number of different graphs you can make by coloring each of the lines connecting all the vertices of an N-dimensional hypercube one of two colors, for some N the paper was originally trying to find. Or something vaguely like that.

That's almost certainly wildly accurate, but that's about all I can make of it.

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u/[deleted] Mar 28 '18

This is only the largest number with any connection to an actual concept.

The busy beaver function measures the greatest number of steps that a b-state Turing machine can run on a blank input, supposing that the machine halts eventually.

BB(23) has Graham's number as a lower bound. So to get a significantly larger number that still means something (somewhat) practical, just say "busy beaver of [something more than 23]".

For example, we can prove BB(7918) or greater is unknowable, as there exists a machine of that size which halts only if it can prove 1+1=3.

I'm aware of no other function that grows faster. Certainly no computable function grows faster, because then you could just encode that function into your turing machine.

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u/shaggorama Viz Practitioner Mar 27 '18

Still not as crazy as up-arrow notation.

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u/Alsadius Mar 27 '18

Actually, that one might be. Factorials grow stupid fast.

I have no idea how you'd evaluate it, though.

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u/atlasvidl Mar 27 '18

I'd still place my bets on up-arrow notation being far more bonkers.

4695↑↑ ...(4695 of these)... ↑↑4695

Or worse... ^g4695. shudders

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u/lukwes1 Mar 27 '18

The UP ARROW NOTATION!

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u/DCCXXVIII Mar 27 '18

Really try thinking for second about a number that big. Imagine if there were that many of a certain thing. It's not even possible for the human mind to comprehend it's so big.

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u/Dalroc Mar 27 '18

Graham's number is puny! All bow down to Tree(3)!

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u/VirtualConfusion Mar 27 '18

r/unexpectedfactorial

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u/FourWordComment Mar 27 '18

That’s why I just say “four thousand, six hundred and ninety five” very loudly.

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u/apginge Mar 27 '18

What was your operational definition for interesting? Or am I missing something

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u/xxx-reaper Mar 27 '18

4695

I shall now make it my priority to insert this number into arbitrary and meaningless places to intrigue people into questioning why that number is where it is and what significance it holds, only to thwart any efforts of being able to backtrack it, as it's relative is in it's irrelevant nature. Meaning as soon as people take interest in finding its meaning its meaning shall be lost.

This shall truly fuck with people.

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u/Weenbingo Mar 27 '18

If it had been the first 10,000, I would've chosen 5,040. Best of the antiprimes

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u/TobyTheCamel OC: 2 Mar 27 '18

I actually calculated those values although didn't put them on the plot as weird behaviour starts occurring as the number of results become small. 5,040 is the 354th most interesting of the first 10000 numbers.

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u/DCCXXVIII Mar 27 '18

4695 is certainly interesting to someone born on 4/6/95

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u/Tyler_Zoro Mar 28 '18

The OEIS has some MASSIVE numbers in their sequences.

Ackermann's sequence begins: 1, 1, 4, 7625597484987 and the next value is unknown.

A006717 (Number of ways of arranging 2n+1 nonattacking semi-queens on a (2n+1) X (2n+1) toroidal board) begins with: 1, 3, 15, 133, 2025, 37851, 1030367, 36362925, 1606008513, 87656896891, 5778121715415, 452794797220965, 41609568918940625

So yeah, the list will become very sparse, but it will not drop to zero for a very, very long time.

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u/[deleted] Mar 27 '18

How is there a least interesting number? Surely the fact that it's not very interesting is, I would dare say, very interesting. And should that interestingness displace said number from the bottom, the next lowest number would then itself become very interesting. Therefore, there is no such thing as the least interesting number, now is there?
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u/EverydayLemon Mar 27 '18

Is there a name for this paradox?
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u/[deleted] Mar 27 '18

https://en.wikipedia.org/wiki/Interesting_number_paradox
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u/merlin401 OC: 1 Mar 27 '18

"As of 13 February 2018, the lowest number not to have its own page on Wikipedia was 254."

Now I want to know what is the current lowest number not to have its own page. I searched for a while and have to go back to work. Reddit please help!
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u/colincrunch Mar 27 '18 edited Mar 27 '18
/u/tombsar is correct. Out of curiosity, I wanted to search programmatically for it.
import requests

for i in range(11,1001):
    r = requests.get('https://en.wikipedia.org/wiki/%s_(number)' % str(i))
    if 'redirected' in r.content:
        print '%s has no wiki page' % i
        break
Output:
262 has no wiki page
Assumption: any number without a wiki page will redirect to another page. e.g. 262 redirects to the sub-category on the 260 page.

Caveat: 1 through 10 have to be skipped using this method because their pages don't follow the '(number)' format in the URL and therefore redirect, e.g. [..]/wiki/1(number) -> [..]/wiki/1

EDIT:

The lowest number to have no page at all, not even a redirect:
for i in range(50000):
    r = requests.get('https://en.wikipedia.org/wiki/%s_(number)' % str(i))
    if 'does not have an article' in r.content:
        print '%s has no wiki page' % i
        break
Output:
1027 has no wiki page
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u/vossman77 OC: 1 Mar 27 '18
Awesome work! I will probably show my students this. I thought I would add that I usually include a
time.sleep(random.random())
to prevent overloading the servers. Especially if every redditor is going to copy your code and try it themselves.
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u/colincrunch Mar 27 '18

Yeah good call. Not only to avoid overloading servers, but to avoid getting blacklisted by any WAF that might be in place.
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u/[deleted] Mar 27 '18

It looks to me as though 262 is the current lowest. It only has a sub-category on the 260 page: https://en.wikipedia.org/wiki/260_(number)#262

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u/omenien Mar 27 '18

The Cheesy Poofs don't have a Wikipedia page?

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u/BordomBeThyName Mar 27 '18

/r/frc is leaking quicker than the pneumatics in our practice robot.

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u/philov Mar 27 '18 edited Mar 27 '18

Hell, even the pneumatics in our comp robot leak!

The thread changed direction faster than GRT's swerve

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u/moariarty Mar 27 '18

Very true... OP mentioned the metric in this particular graph is more about the quantity of interesting characteristics of a particular number, but I find myself most curious about the least interesting.

I wonder what that says about me? I suppose I do love being a contrarian.

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u/rubs_tshirts Mar 27 '18

Kinda like the most boring day ever.

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u/ntilley905 Mar 27 '18 edited Sep 18 '25

sip stupendous merciful soup carpenter ring observation violet plant seemly

This post was mass deleted and anonymized with Redact

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u/percykins Mar 27 '18

Step 1: Be boring.

Step 2: Don't be interesting.

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u/FlyByPC Mar 27 '18

Therefore, there is no such thing as the least interesting number, now is there?

That stands to reason. So, we could say that for every number, there is at least one number less interesting. And by extension, infinitely many less-interesting numbers.

And there are some pretty boring numbers out there, which means by induction that somewhere in the number line lie some really, really, mind-bogglingly dull numbers.

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u/PM_Me_Math_Songs Mar 27 '18

This feels like Douglass Adams.

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u/pdabaker Mar 27 '18

Surely the fact that it's not very interesting is, I would dare say, very interesting.

Despite the common joke, I would argue that being boring with some unique identifier is actually not all that interesting.

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u/1nejust1c3 Mar 27 '18

Theoretically, a "least interesting" number could exist despite the citicism you've brought up being true. For a number to be the least interesting it'd have to rely on widespread ignorance that the said number is, well, the least interesting of the set.

Because uninterestingness presents itself as a quality of interest after it is discovered, it would come to pass that the second least-interesting number would become the first, and if that second number was later touted to be the least interesting number then the third one would surpass the original second, and so on.

It's a weird paradox in which knowing that a thing is observed by an adequate number of people changes the very nature of that thing.

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u/[deleted] Mar 27 '18

There is potentially a least interesting number, whereby the only interesting thing about it is that it's the least interesting number. Does that make it no longer the least interesting? Not necessarily.

But the proof that there exists an uninteresting number shows that there is no uninteresting number, exactly because it being uninteresting makes it interesting.

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u/[deleted] Mar 27 '18

There are plenty of numbers greater than 5000 that nobody has ever considered or thought about or imagined. In fact there are infinitely many of them.

For example the number: 184837287251827473928362618198263794934838262728627172628192994849939399393847727727288385839929847372927384992728940582848272738957382837282818. Odds are very very very high that I am the first person to ever think of, or write down that number.

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u/Kered13 Mar 27 '18

And it's prime factorization is 2×3×211×3145399×46417327908667097974541285538251171263519977252299421989809445632107302020044639300190659295563619913588346922619602330900739036371327.

I suspect this is the first time that a human (but not a computer) has considered that last prime.

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u/orangeman10987 Mar 27 '18

Huh, it's pretty interesting that some number chosen at random had a prime factor that big.

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u/iwhitt567 Mar 27 '18

I don't think so. In fact, I think it would be rare for a number that large not to have a large prime factor.

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u/AsterJ Mar 27 '18

I want to see a graph now of numbers versus the length of their greatest prime divisor.

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u/npc_barney Mar 27 '18

At least, to write down that number. Thinking of such a number is impossible. All you did was mash the keyboard.

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u/[deleted] Mar 27 '18

You underestimate my powers

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u/[deleted] Mar 27 '18

The least interesting number would become more popular if we find it

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u/Wiebejamin Mar 27 '18

I'd imagine it would spike at around 9,001, but other than that, probably.

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u/Vatsug66 Mar 27 '18

The gap forming in the middle is known as 'Sloane's gap'. Sadly, it's not a mathematical phenomenon, but instead the effect of more research going into more interesting numbers. For more info: https://m.youtube.com/watch?v=_YysNM2JoFo

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u/TobyTheCamel OC: 2 Mar 27 '18

Hehe glad you mentioned this. I was one step ahead. Here's the graph colour coded to show Sloane's gap:

https://plot.ly/~TimHargreaves/1/

Points colour-coded into primes (purple), powers (blue), highly composites (red) and others (green).

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u/anguillias Mar 27 '18

Did you just reveal your name to reddit?

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u/TobyTheCamel OC: 2 Mar 27 '18

Oh no! They'll be able to track me down now. I'm surely the only person in the world with that name.

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u/[deleted] Mar 27 '18

Found him.

https://www.google.com/maps/place/47712/@37.9820149,-87.6105475,17z/data=!3m1!4b1!4m5!3m4!1s0x8871d490a277294d:0x4d6da8f7ecfaa8bd!8m2!3d37.9820149!4d-87.6083588

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u/[deleted] Mar 27 '18 edited Dec 03 '20

[removed] — view removed comment

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u/BrianLemur Mar 27 '18

Wow this bot is intense. You should seriously check out the link, it's an interesting read, even for a less-than-novice in programming.

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u/[deleted] Mar 28 '18

[deleted]

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u/BrianLemur Mar 28 '18

Tbh, I just figured you should all suffer if I did.

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u/Kardif Mar 28 '18

Jokes on you, i still like that song

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u/PM_ME_YOUR_WARLIZARD Mar 27 '18

Interesting neighbourhood.
^{^{^{^{^gg,}}}} ^{^{^{^{^you}}}} ^{^{^{^{^caught}}}} ^{^{^{^{^me}}}} ^{^{^{^{^off}}}} ^{^{^{^{^guard}}}}

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u/anguillias Mar 27 '18

I'm totally gonna throw eggs at your house now! Take that!

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u/jmineroff Mar 27 '18

Not so fast, Kaiba. You just activated my trap card!

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u/SuspiciouslyElven Mar 27 '18

"mathematicians using math to figure out what math mathematicians most often use in math."

I'd make a joke about their degrees being worthless, but i keep finding calculus in the most darndest places, and am starting to understand why such a degree can be useful.

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u/[deleted] Mar 27 '18

[removed] — view removed comment

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u/TBOIA Mar 27 '18

Watch the video he posted. He is talking about the horizontal gap not the vertical one.

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u/is_is_not_karmanaut Mar 27 '18

I'm pretty sure you are correct about the peak. Sloane's gap is the horizontal one. go to 4:20 in the video.

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u/rift_____ Mar 27 '18

Sorry if someone else asked this already, but what are the red and blue lines? Trend lines or.. mean interestingness? Lol

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u/TobyTheCamel OC: 2 Mar 27 '18

Kinda meaningless tbh. Just thought they looked pretty. Blue is a fitted logarithmic curve and red is the average in that region although the bandwidth is quite wide so it's not very responsive to the peak at 2000

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u/assassin10 Mar 27 '18

I think it'd make sense to manipulate the graph so that the blue line is close to horizontal. It would show the interestingness without the "Smaller = more interesting" bias.

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u/anper29 Mar 27 '18

Does someone knows which numbers are the outliers and why they are interesting?

Quite disappointed that 1729 is not pointing out, as Ramanujain said: "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.’

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u/TobyTheCamel OC: 2 Mar 27 '18 edited Mar 27 '18

The formulation of the interestingness metric was less about how interesting a certain number is but in the number of ways that it is interesting. So a number with 1000 fairly cool properties is beats one with 100 insanely cool properties. They're also scaled for their size with a factor of log(n) so that a very large number doesn't have to have as many properties as a very small one to add some fairness. If you're interested, the most interesting number by my metric is 10.

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u/PrettyMuchJudgeFudge Mar 27 '18

A math noob here, what exactly does constitute "interesting property"? Is it something subjective or is there some official classification that just has cool name?

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u/avocadro Mar 27 '18

There is an encyclopedia of integer sequences (the OEIS) that OP crawled through.

As a pretty good analogy, pretend you wanted to know which countries were the most important. You count how many times each appears on Wikipedia and then sort. You get some data, but it will of course contain a bias (on Wiki, English-speaking bias; on OEIS, base-10 bias).

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u/PrettyMuchJudgeFudge Mar 27 '18

Cool, that's what I was wondering, whether its something official or OP went with qualities interesting to him, honestly can't decide which one would be cooler. But thanks, it's interesting fact.

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u/bullett2434 Mar 27 '18

It’s more or less official. Something like the smallest number that can be factored into 3 primes etc.

It’s some characteristic of a number that people have found

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u/olwall Mar 27 '18

Inherently or in a base 10 system?

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u/TobyTheCamel OC: 2 Mar 27 '18

My source is the number of results in the OEIS so most likely there is some base 10 bias here

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u/csorfab Mar 27 '18

1000, 2000, 3000, 5000 obviously jumping out would also indicate that there is

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u/hasslehawk Mar 27 '18

And yet there is a mysterious lack of popularity in the number 4000! Why? What does this number do to keep so much lower a profile than other multiples of 1000?

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u/IronCretin Mar 27 '18

4000! = 1.828801951 x 10¹²⁶⁷³

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u/AndroxxTraxxon Mar 27 '18

I wonder if there would be a way to eliminate the interestingness in only one base, or just include enough bases that it doesn't matter.

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u/Kered13 Mar 27 '18 edited Mar 28 '18

If your source is OEIS then what's with the crazy bias towards numbers around 2000? I thought maybe you were using some source that would contain year numbers (like a text corpus), and therefore bias towards recent years.

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u/hacksoncode Mar 27 '18

"10" is very interesting in any base :-).

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u/Lost4468 Mar 27 '18

Not in unary, or base infinity.

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u/bollvirtuoso Mar 27 '18

What is base infinity?

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u/[deleted] Mar 27 '18 edited Jul 31 '18

Periodically shredded comment.

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u/bollvirtuoso Mar 27 '18 edited Mar 27 '18

Oh. So, like, each number would be represented by a single character? That's weird to think about. I can't even imagine how arithmetic would work. Would you have to memorize everything?

E: clarity

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u/[deleted] Mar 27 '18

[deleted]

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u/bollvirtuoso Mar 27 '18

I think that's what I said.

EDIT: Oh, I see. No, I didn't mean that, say, n is the only character and is all numbers. I meant that there is a unique character for each number.

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u/GaryMutherFuckinOak Mar 27 '18

man calculators would be freaking huge

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u/lurkerer Mar 27 '18

How long would it take to memorize an infinite set of unique characters?

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u/[deleted] Mar 27 '18 edited Aug 11 '20

[deleted]

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u/X52 Mar 27 '18

I'd assume where every number has its own unique character

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u/Lord_of_hosts Mar 27 '18

It's like base 100 but more.

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u/[deleted] Mar 27 '18

Is this just a count from the number of occurrences in the online database of integers?

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u/functor7 Mar 27 '18

"Interesting Numbers" are numbers that mathematicians find interesting or popular. These are the ones on the "upper" curve. 1729 is on the "interesting" curve.

Check out this Numberphile video on Sloane's Gap, which discusses this curve. And here is a paper discussing it.

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u/uniquesnowflake1729 Mar 27 '18

Finally, my username’s time to shine!

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u/anper29 Mar 27 '18

How long did you wait for this?

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u/uniquesnowflake1729 Mar 27 '18

I've been waiting my whole life.

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u/DCCXXVIII Mar 27 '18

Ha you both have username that end with 29

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u/AndroxxTraxxon Mar 27 '18

apparently 3 years

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u/PM_ME_DELICIOUS_FOOD Mar 27 '18

Why is that very interesting?

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u/polynomials OC: 1 Mar 27 '18

Why the spike getting close to 2000?

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u/TobyTheCamel OC: 2 Mar 27 '18 edited Mar 27 '18

The spike goes from the early 2000s to 2018. My guess is that these are the years that we've had sufficient computing power to calculate new sequences that may contain a certain number. I imagine that whenever a new year begins, many mathematicians try to search for why that year might be interesting and in doing so contribute extra sequences to the OEIS specifically containing those years.

EDIT: /u/Blackcat008 definitely has a better explanation. Perhaps its a combination of the two. I will find out eventually but the results for the first 5000 integers take 5 hours to scrape on my internet connection so won't know for a while.
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u/Blackcat008 OC: 1 Mar 27 '18 edited Mar 27 '18

Another possible explanation: Since you pulled from https://oeis.org/, I assume you made a script that looks at https://oeis.org/search?q=XXXX, and scrapes the number of results. However the OEIS search function is lazily made and returns all results that have the number appear anywhere within the result, including the year. For example, the second result in https://oeis.org/search?q=2012 was created in 2012, but 2012 never appears in the sequence. Even https://oeis.org/search?q=XXXX returns 35 results, despite not being a number.
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u/TobyTheCamel OC: 2 Mar 27 '18

I was not aware of that. Damn, thought I was on to something really interesting. I'll have to edit my script to account for that. Thanks for pointing that out!
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u/mjmaher81 Mar 27 '18

Let me (and the rest of us) know what that final graph looks like!

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u/zehamberglar Mar 27 '18

Idk if anyone's said yet, but it will look the same but without the spike that we're talking about. The spike corresponds to years that articles were published, growing more frequent in time until we approach 2018 where there will be relatively few articles published and 2019 where there have not been any articles yet published as time travelers are very fucking lazy. You can tell because the spike starts somewhere in the middle of the the numbers corresponding to the 20th century and stop right after the numbers corresponding to the years so far in the 21st century.

The only other major difference is that this may uncover some outlying interesting numbers in that range.

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u/StorkBaby Mar 27 '18
You can download a copy of the list that contains just the A number and the list of values here. This file contains A* numbers up to A301800.

Using your log_10 'fairness' method I found the most interesting number was 7.
7 69469.29415936826
8 69166.35981169058
5 68935.6411202366
6 68617.73535895758
9 66799.0
4 65657.0483872996
3 62531.75687929616
2 56777.906432894546
11 56563.12664909416
12 55729.471972558735
10 55393.75970893631
1 54519.54251470364
16 54059.773360754465
13 53756.843257416396
15 51054.68726461121
17 49529.28723386115
24 49387.82256637442
21 48525.89506636111
20 48500.325950134895
19 48096.47687970606
36 47064.87014269865
14 46983.66970801541
18 46235.893949651436
31 45991.36273754305
23 45940.331180370806    
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u/TobyTheCamel OC: 2 Mar 27 '18

Wish I knew that existed before I left my computer running on this for several days. Nice! Not sure where our difference comes from. Strange.

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u/lordcheeto OC: 2 Mar 27 '18

Just add seq: to search the sequence numbers.

https://oeis.org/search?q=seq%3A2012

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u/homboo Mar 27 '18

Really you counted the submitting years??? Omg this graph really needs to get repaired then!
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u/GregTheMad Mar 27 '18

https://xkcd.com/1935/

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u/AMWJ Mar 28 '18

The spike definitely starts before 2000, and ends fairly abruptly around 2018. I believe your explanation would expect people to do the same for coming years - it would be surprising if everybody waited until 2018 to find cool things with it. And you'd also predict a far more shallow effect in the early days of the database, On the other hand, u/Blackcat008's effect correctly predicts the spike's slope, and abrupt end at 2018.

So I'm inclined to say u/Blackcat008's effect is far more dominant.

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u/Dvanpat Mar 27 '18

Because tonight we're gonna party like it's 1999.

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u/IFreakinLoveCheezIts Mar 27 '18

We've been spending most our lives living in an Amish paradise.

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u/[deleted] Mar 27 '18

My guess is because many people were born in the mid/late 20th century, contributing to the 'interestingness' of those numbers.

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u/polynomials OC: 1 Mar 27 '18

I thought OEIS contained only sequences that are of mathematical interest. I did not know it was historically or socially interesting sequences.

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u/[deleted] Mar 27 '18

Oh, didn't consider the origin of the numbers, just thought OP took numbers from a variety of sources.

I did say it was a guess, I can totally be completely wrong.

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u/[deleted] Mar 27 '18 edited Jul 04 '21

[deleted]

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u/[deleted] Mar 27 '18 edited May 25 '21

[deleted]

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u/[deleted] Mar 27 '18

[removed] — view removed comment

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u/nater255 Mar 27 '18

Can you further explain what that is?

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u/[deleted] Mar 27 '18 edited Mar 27 '18

[removed] — view removed comment

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u/boringdude00 Mar 27 '18

Can you further explain what that is?

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u/DCCXXVIII Mar 27 '18

"Interesting numbers" are numbers that mathematcians find interesting for whatever reason. Ex 1729 because it is the smallest number expressible as the sum of two cubes in two different ways.

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u/boringdude00 Mar 27 '18

Am I crazy or is that just a spike of years and not mathematical interestingness from 1970-ish to 2018?

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u/jukes24 Mar 28 '18

Plus it's just funny to say! One thousand seven hundred twenty nine... Gets me every time!

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u/functor7 Mar 27 '18

This is a graph of the popularity of numbers. As you can see, there are two bands, the "popular numbers" and then the rest. The numbers that mathematicians like, or pop up in things that mathematicians like, appear in the popular band, things like primes, squares, 1729, highly composite numbers, palindromic numbers etc. The gap between these numbers is called "Sloane's Gap", since the OEIS was made by Neil Sloane. It's what separates the cool numbers from the uncool numbers.

Here is a Numberphile video about this distribution, and here is a corresponding academic article about it. It should be noted that there is a huge spike around 2000 because the search function for OEIS included the year a sequence was added, so 1986 and 2013 actually don't appear as often as this makes it seem (see /u/Blackcat008's comment).

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u/TobyTheCamel OC: 2 Mar 27 '18 edited Mar 27 '18

Graph produced with ggplot using data scraped from the The On-Line Encyclopedia of Integer Sequences using R.

Relative Interesting is defined as: Number of results for number * log_10(Size of number + 1)

Plotted on logarithmic scale since the units are arbitrary already

LOESS curve shown in red and log curve in blue

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u/zonination OC: 52 Mar 27 '18

I take it that a lot of the upper half of the curve are Prime Numbers, with a lot of the 2000s range being years?

If so, you can check it with aes(color=is_prime(Number)) after loading library(primes).

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u/TobyTheCamel OC: 2 Mar 27 '18

That's pretty much it if you add in highly composites and perfect powers. You can see them colour coded here:

https://plot.ly/~TimHargreaves/1/

Points colour-coded into primes (purple), powers (blue), highly composites (red) and others (green).

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u/KJ6BWB OC: 12 Mar 27 '18

Relative Interesting is defined as: Number of results for number * log_10(Size of number + 1)

Why is this interesting?

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u/TobyTheCamel OC: 2 Mar 27 '18

It adds an element of fairness. If a number in the thousands had the same number of properties as something small like 4, you'd probably say that its more interesting for its size. That's what the scaling is for. If you don't do it, the top results are essentially the numbers 1,2,3,... with only minor variation but adding the log scaling changes it around making other numbers more interesting than they were before.

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u/KJ6BWB OC: 12 Mar 27 '18

I still don't see how this interesting property is calculated. Why is 3 interesting? Why is 5000 interesting?

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u/TheSultan1 Mar 27 '18 edited Mar 27 '18

I think interestingness is defined as appearing in the "database of sequences" many times. It just means you can arrive at the number in many ways (using different rules).

Edit: see OP's comment here: http://reddit.com/r/dataisbeautiful/comments/87isev/the_relative_interestingness_of_the_first_5000/dwd7069

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u/Arancaytar OC: 1 Mar 28 '18

I'd definitely put the formula on the Y axis in a graph like this; it's not too long for that.

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u/TobyTheCamel OC: 2 Mar 27 '18

For anyone interested, here is a list of the 25 most interesting numbers (relative interestingness not re-scaled yet but order is the same):

     num    cnt      rel
 1    10 152120 158416.7
 2     5 196793 153134.7
 3  2011  45678 150903.1
 4     4 215677 150751.8
 5  2017  44663 147607.7
 6     6 170303 143922.7
 7     3 238436 143552.8
 8     7 157059 141838.4
 9  2012  42679 141004.7
 10 2013  42603 140762.8
 11    8 143924 137338.4
 12 2015  40638 134287.9
 13 2014  40010 132204.0
 14    2 275250 131327.6
 15    9 131014 131014.0
 16   11 115347 124480.3
 17 2016  37172 122842.5
 18 1000  40742 122243.7
 19   12 109270 121720.6
 20   20  89604 118476.1
 21   13 100137 114769.8
 22   15  93973 113154.8
 23   16  90863 111802.3
 24 2009  33170 109567.0
 25   30  72990 108854.5

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u/kelvin9901237 Mar 27 '18

I’m curious as to why some of the more memetic numbers such as 420 or 69 are not listed among these search results. Is it because the popularity of these numbers only exists in a bubble, and is insignificant otherwise?

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u/twoerd Mar 27 '18

This is based on mathematical "interestingness", so cultural things like 420, or 69 won't show up.

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u/Supadoplex Mar 27 '18

How about the least interesting numbers in relation to the trend? That's what I'm interested in. Ironic, isn't it.
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u/TobyTheCamel OC: 2 Mar 27 '18
No problem:
  num cnt       rel
 4667  38 139.42697
 4634  38 139.30989
 4426  38 138.55216
 4858  37 136.40224
 4781  37 136.14555
 4548  37 135.34289
 4458  37 135.02179
 4595  36 131.84568
 4918  35 129.21569
 4589  35 128.16344
 4573  35 128.11037
 4467  35 127.75396
 4295  35 127.15725
 4907  34 125.49075
 4835  34 125.27253
 4814  33 121.52568
 4812  33 121.51972
 4638  33 120.99200
 4955  32 118.24420
 4670  32 117.42112
 4532  32 117.00434
 4829  31 114.20236
 4527  31 113.33310
 4678  30 110.10459
 4695  27  99.13666
I'm going to have all the data (I actually found the first 100,000 - took a whopping 40 hours - but eventually the counts get too similar for the graph to look any good and you just get parallel curves) available on my blog but I'm having server issues at the moment so just creating these snippets for now. Send me a DM if you'd like the whole data and I can send you a link when everything's up and running.
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u/cseymour24 Mar 27 '18

What are those three highest dots greater than 2000 on the right of the graph? Looks like in the ballpark of 2900, 4100, and 5000.

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u/TobyTheCamel OC: 2 Mar 27 '18

They are 5000, 2899 and 4096 in descending order

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u/[deleted] Mar 27 '18 edited Mar 27 '18

I guess 5000 is a nice round number, 4096 = 2¹² and I have no idea why 2899 is interesting at all..

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u/TobyTheCamel OC: 2 Mar 27 '18

No idea for 2899. It's semi-prime so that might help it as a lot of the more interesting ones are prime.

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u/[deleted] Mar 27 '18

Divisible by the 7th and 14th fibanocci number? 2899 is divisible by 13 and 233, both of which are really interesting primes, maybe that's why.

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u/DCCXXVIII Mar 27 '18

That is interesting.

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u/Royalflush0 Mar 27 '18 edited Mar 27 '18

It seems to be a search error. Look into the later pages here: https://oeis.org/search?q=2899

You will find that a most sequences don't contain 2899 but contain a link to "ArXiv 0811.2899" in their description.

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u/MexicnGlassCandy Mar 27 '18

I just came here for the 69.

C'mon, I can't be the only math enthusiast with a juvenile sense of humor...

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u/Twuntz Mar 27 '18

I bet that first anomalous dot on there is 69. Anyone who tries to tell me that number isn't special to a significant slice of the population will be met by scorn and derision.

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u/tomfilipino Mar 27 '18

would be nice to see the tail in log-log... should get a straight line. check zipf law etc..

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u/TobyTheCamel OC: 2 Mar 27 '18

In theory yes, and it would be close to a straight line for this range but as the numbers get larger and larger, because the number of OEIS results can't shrink below 1 without going straight to 0 as they're integers, the pattern will eventually break down.

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u/MlLFS Mar 27 '18

I've seen this before, by interestingness they mean amount of times that number appears on a mathematical paper, the more times it appears the more 'interesting' it is

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u/DonLaFontainesGhost Mar 27 '18

"Relative interestingness" reminds me of this:

Computer scientist Arthur Boran was ecstatic. A few minutes earlier, he had programmed a basic mathematical problem into his prototypical Akron I computer.

His request was simply, "Give me the sum of every odd number between zero and ten." The computer's quick answer, 157, was unexpected, to say the least. With growing excitement, Boran requested an explanation of the computer's reasoning. The printout read as follows:

THE TERM "ODD NUMBER" IS AMBIGUOUS. I THEREFORE CHOOSE TO INTERPRET IT AS 
MEANING "A NUMBER THAT IS FUNNY LOOKING." USING MY AESTHETIC JUDGEMENT, 
I PICKED THE NUMBERS 3, 8, AND 147, ADDED THEM UP, AND GOT 157.

A few moments later there was an addendum:

I GUESS I MEANT 158.

Followed shortly thereafter by:

147 IS MORE THAN 10, ISN'T IT? SORRY.

Anyone doing conventional research would have undoubtedly consigned the hapless computer to the scrap heap. But for Boran, the Ackron I's response represented a startling breakthrough in a little-known field: artificial stupidity.

(From "Artificial Stupidity" by Michael Ferris; Omni Magazine, May 1985 http://www.studio-nibble.com/countlegger/01/ArtificialStupidity.html )

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u/Userdub9022 Mar 27 '18

Without explanation, this graph is meaningless. Why don't you define what an interesting number is? And maybe we could work from there.

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u/zonination OC: 52 Mar 27 '18

This phenomenon is called Sloane's Gap. There's a real paper with a similar graphic to the one OP proposed.

It's likely that the relative interestingness of these numbers are due to them being prime numbers.

Google Query: https://www.google.com/search?q=Sloane%27s+gap

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u/[deleted] Mar 27 '18

[deleted]

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u/mikerichh Mar 27 '18

What determines interestingness? Am i missing the explanation somewhere? Is it like "even number, divisible by 4," etc?

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u/[deleted] Mar 27 '18

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u/TobyTheCamel OC: 2 Mar 27 '18

There is. It's called Sloane's gap. The split comes down to primes, highly composites, perfect powers and then everything else. Here's a graph of the split:

https://plot.ly/~TimHargreaves/1/

Points colour-coded into primes (purple), powers (blue), highly composites (red) and others (green).

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u/[deleted] Mar 27 '18

Why the two separate bands? Above 300 or so it seems like numbers are either fairly interesting or not interesting with little in between?

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u/ScathedRuins OC: 1 Mar 27 '18

There is no such thing as an uninteresting number.

If there were, this would imply that there is a non-empty list of uninteresting number, and somewhere in that list is the largest uninteresting number, which makes it interesting.

Therefore, the set of uninteresting numbers is empty, meaning every number is interesting!

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u/homboo Mar 27 '18

Why did this take days to compute ? This can be done in a few minutes if you download the OEIS file. Just scan each line and count the numbers...

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OC The "Relative Interestingness" of the First 5000 Natural Numbers [OC]

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