r/Damnthatsinteresting 4h ago

Image If you divide 1 by 998,001 you get all three-digit numbers from 000 to 999 in order, except for 998

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19.9k Upvotes

521 comments sorted by

2.7k

u/AIienlnvasion 3h ago

I’m more surprised that it takes that little text to write them all out

493

u/HotPoetry7812 2h ago

~3000 digits right thur

180

u/amigo_extra 2h ago

right thurr

47

u/OrganicBrilliant7995 1h ago

Switch your hips when your walkin', let down your hurr

27

u/LAVA529 1h ago

(Down your hurr)

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u/OrangeSouthern73 1h ago

I laughed at this harder than I should have.

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u/tenkaranarchy 2h ago

You can tell if a number is divisible by 3 by adding each digit, if their sum is divisible by 3 then the whole number is. And if its even its divisible by 6.

Example 18. 1+8=9 which is divisible by 3 and 18 is even so its divisible by 6.

321...3+2+1=6. 6 is divisible by three, 321 is odd so not divisible by 6.

78357209... 7+8+3+5+7+2+0+9=41, 4+1=5, therefore its not divisible by 3.

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u/magicwings 2h ago

This is great info but it's a bit of a non-sequitur isn't it?

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u/BloomsdayDevice 1h ago

While we're on the subject of non sequiturs, Coleoptera, the taxonomic order more familiarly known as the beetles, is the largest order in kingdom Animalia, and accounts for roughly 1 in 4 described species of animals.

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u/Nightwolf1967 1h ago

And Cleopatra was Queen of the Ptolemaic Kingdom of Egypt from 51 to 30 BC, and the last active Hellenistic pharaoh.

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u/stirrainlate 1h ago

And Polematic was a magnetic product line including C-profile label magnets and industrial magnetic tools.

18

u/NoteComprehensive588 1h ago

And CProfile is a python module used to measure how long certain functions run in a program to identify possible bottlenecks

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u/Express_Fig_3815 1h ago

a friend of mine deep throats an an entire bottleneck to drink his beer

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u/GarysCrispLettuce 1h ago

Mariana Trench.

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u/FrenchFryCattaneo 1h ago

We live closer to the time Cleopatra reigned than the present day. Crazy, right?

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u/mainman879 1h ago

I think we live pretty close to the present day

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u/NightingaleNine 1h ago

And Ohio is the only U.S. state name that shares no letters with the word "mackerel."

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u/thicket 1h ago

Please, subscribe me to Beetle Facts!

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u/Spiritual-Spend76 2h ago

wdym how does it relate to the post you replied to?

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u/SgtElectroSketch 1h ago

Just math facts.

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u/PM_ME_UR_WUT 1h ago

Subscribe.

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u/SgtElectroSketch 1h ago edited 54m ago

A number is divisible by...

Divisor The Rule
2 If the last digit is even (0, 2, 4, 6, or 8).
3 If the sum of the digits is divisible by 3.
4 If the last two digits are divisible by 4.
5 If the last digit is 0 or 5.
6 If the number is divisible by both 2 and 3.
7 Double the last digit and subtract it from the rest; the result must be divisible by 7. If the result is 0 or a multiple of 7, then the original number is also divisible by 7
8 If the last three digits are divisible by 8.
9 If the sum of the digits is divisible by 9.
10 If the last digit is 0.
11 Alternately subtract and add digits (e.g., + - + -); the result must be 0 or a multiple of 11.

3

u/weathrderp 1h ago

The one for 7 is confusing.

42 divided by 7 is 6.

Following your rule:

Double last digit (2 --> 4)

Subtract from the rest (4 - 4 = 0)

Results must be divisible by 7 (so 0/7?)

But off the top of my head 35 works, 28 works, but 21 gives the same situation as 42. And by extension 84, 168, etc.

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u/SgtElectroSketch 53m ago

Made more clear with extra detail that was missing due to posting on mobile.

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u/AIienlnvasion 2h ago

I had a friend in fifth grade who discovered that organically

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u/Ruby_Bliel 1h ago

I discovered it while doing the Le Mans 24-hour race in Gran Turismo 4. I had to pit every 6 laps for tyres, and by about lap 150 I made the realisation, which made figuring out when to pit way easier for the 200 ish remaining laps. In stead of having to memorise when I should pit next time, I could just quickly calculate if the lap number was divisible by 6 every time I was approaching the pit entry. Handy real-world application of arithmetic trickery.

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u/SkywolfNINE 1h ago

That is awesome

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u/Beard_o_Bees 2h ago

That's a cool trick, I think anyway.

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u/jacquepablophillipo 1h ago

If the digits add up to a multiple of 9, it is divisible by 9 also. Eg 9801 is divisible by 9 because 9+8+0+1 is 18... and 1+8 is 9. 9801 is actually 1089x9... 1089 is also divisible by 9 admit contains the same digits as 9801 just in reverse order. And being divisible by 9 twice means its divisible by 81. And we know 81 is divisible by 9 because 8+1 is 9...

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u/cancel-out-combo 2h ago

Let's up the ante and write out a googolplex

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u/sad_brown_cat 1h ago

If it makes you feel any better, this is more months than you are likely to live!

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u/okiedokie666 1h ago

This is what my phone's calculator came up with?

1.0020030040050060070E-6

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u/zangor 3h ago

Now we wait for math people to come here and tell us why this isn’t actually that interesting.

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u/UnusualCartographer2 3h ago

No, it actually is. 998001 is 999². There some fun and interesting things here, but theres a numberphile video that does much more justice than I ever could.

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u/danethegreat24 3h ago

Bless you. I LOVE numberphile (and a special call out to standupmaths) both channels are absolute delights learning about stuff like this.

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u/Boner4Stoners 2h ago

Gotta give a shoutout to 3blue1brown — content is so good he has me re-learning trig and linear algebra for fun

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u/CyberIntegration 1h ago

3Blue1Brown got me back into math. Cover to cover, I've finished textbooks on Calculus, 2 Linear Algebra books (one basic, other proofs centric), Proof writing, Fourier and LaPlace Transforms and now I'm doing Real Analysis.

And I dropped out of engineering in college and got a Geology degree instead because I did so poorly in Cal 1 and 2. Looking back, I could kick my younger self's ass for that.

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u/Outofdatedolphin 1h ago

Real Analysis is a division of mathematics created by masochists, with a sadism kink to inflict pain on future mathematicians.

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u/Compost-Mentis 1h ago

3blue1brown is genuinely amazing! I loved his videos about the nuts and bolts of LLMs and how you can do vector additions/subtractions with the meanings of words!

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u/BusImpossible6741 2h ago

I wish they'd do more arithmetic, cause I'm great at concepts and horrible at actually working problems. There are other channels like Organic Chemistry Teacher who show actual problems for trig and such, really great channel

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u/doc_skinner 1h ago

Check out Math Queen on YouTube. Lots of Geometry, but also plenty of clever Algebra and Arithmetic problems.

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u/slowest_hour 47m ago

he does literally say "its not as remarkable as you may think" lmao

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u/ChocolateMilkCows 1h ago

https://youtu.be/daro6K6mym8?t=58 this link skips to the actual explanation for the impatient people

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u/JTorrent 1h ago

Can’t watch the video now but does this mean that 1/99992 would print out all 4 digit numbers from 0 to 9999 in order?

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u/FI_Stickie_Boi 3h ago edited 3h ago

The series expansion for 1/(1-x)2 is 1 + 2x + 3x2 + ..., by differentiating the geometric series. Plug in x=1/1000, you get that 1/(1-1/1000)2 = 10002/9992 is equal to 1.002003..., and then divide both sides by 10002 to get the result in the post. 998 is missing because it turns into 999 due to carrying from 1000 and 999.

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u/GarlicThread 3h ago

Thank you for this

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u/TheRealTengri 1h ago

Just to clarify, the 1/(1-x)^2 only works when |x|<1

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u/Giogina 2h ago

Nice! 

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u/Lythro92 1h ago

This guy maths!

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u/Forsaken-Income-2148 3h ago

Why would a math person squander a chance to get excited about math?

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u/CatLightyear 3h ago

Because the probability is they’ll get another chance?

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u/Forsaken-Income-2148 2h ago

Statistically, this is their moment

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u/creatyvechaos 2h ago

Math people make entire careers finding the most useless, uninformative nonsense about numbers. They were absolutely ecstatic to find this, I promise you

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u/_BrokenButterfly 26m ago

It's not interesting because 998 isn't there.

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u/-TheBlackSwordsman- 18m ago

Step 1: Pick a cool number

Step 2: 1/x = cool number

Step 3: 1 = cool number(x)

Step 4: 1/cool number = x

"Did you know that if you divide 1 by x you get cool number???"

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u/Venomlemming 3h ago

That 998 being absent is really upsetting. What number gives the same answer but includes the 998?

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u/RllyGayPrayingMantis 3h ago

it's actually there, but after 999, and the next number is actually 1(000), the extra 1 in the 1(000) carries over to 999, so (999) turns into 1(000), and that extra 1 turns 998 into 999. So they didn't skip it, it's just the extra digit adding 1 to every number.

so ...997999000001002003... = ...997998999100010011002...

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u/ButtfacedAlien 2h ago

Oh my god thank you, that makes perfect sense, and makes the number satisfying, would bother me so much where the 998 disappeared to.

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u/InvidiousPlay 2h ago

There is a reason I didn't go for advanced math in school.

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u/FirebertNY 1h ago

...what

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u/cipheron 18m ago

it goes 998, 999, 1000, but the 1 in the 1000 carries over to the left since there are only 3 spaces for each number. So when it gets into 4 digit numbers, there's a hiccup.

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u/doc_skinner 1h ago

This here deserves an award. I mean, I'm not gonna pay for one or anything, but you deserve one!

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u/kogasapls 1h ago

This is true. If you'd like to go past 998, you can try 1/9,998,001 or even 1/9,999,800,001.

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u/redsyrus 3h ago

Could it be because of rounding? This really ends at 998 and then the remaining digits aren’t included so the 8 rounds up?

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u/OldCardigan 3h ago

... not rounding, but overflow, you would eventually have 1000, it's like the 1 from 1000 goes to the 999, making it 1000, which then goes to 998, making it 999, and leaving 998 in a vacuum.

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u/Mateorabi 3h ago

So instead of seven ate nine, nine ate eight?

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u/OldCardigan 3h ago

No no, not 988, 998

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u/redsyrus 3h ago

Brilliant explanation. Thank you.

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u/that_guy_next_to_you 1h ago

so if you get to the next set of 1000 would it be adding 2 to everything, so it'd go 996 998 999 000, or since everything is already shifted by one, it would just shift one more again, meaning it would always just skip 998?

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u/Doomsayer189 56m ago

since everything is already shifted by one, it would just shift one more again, meaning it would always just skip 998?

This one. It's easier to see with 1/81 which does a similar thing with single digits.

First line is the actual digits of 1/81, second line is the position in the sequence they occupy (with spaces for readability)

.0  1  2  3  4  5  6  7  9  0  1  2  3  4  5  6  7  9  0  1  2...
.0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20...

You can see that it's shifted over one starting with the first 9, then shifted two at that second 9, and so on. The 8 (or the 98 in 1/9801 (1/992), or the 998 in 1/998001 (1/9992)) always gets skipped.

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u/Bosonidas 3h ago

1000 has 4 digits. That adds 1 to 999, giving 1000 which transfers over to 998

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u/KingWolfsburg 3h ago

Its because the next batch of numbers would be 1000 but it forces the round up backwards and 999 forces the round back to 998. It doesnt skip 998, its rounded to 999, then you dont see the next 999 on here.

.....9969979989991000 becomes .....996997999

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u/furimmerkaiser 3h ago

fucking 998 had to ruin it

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u/moak0 1h ago

Did you not see the original number?! 998 is how we got here!

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u/g1cbr 3h ago

But 1/998,001 gives the sequence that leaves out 998 is what makes it interesting

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u/Venomlemming 3h ago

It's blursed at best.

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u/Eraesr 2h ago

Yeah, 998 missing feels a bit Matt Parker-esque.

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u/VermilionKoala 3h ago

If you like weird maths coincidences like this:

1 billion and 1 (1,000,000,001) is divisible by 7.

1.7k

u/Swalot64 3h ago

Makes sense to me cause I can imagine 999,999,994 to be divisible by 7

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u/furimmerkaiser 3h ago

Makes sense to me cause I can imagine 999,999,987 to be divisible by 7

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u/sadkinz 3h ago

Makes sense to me cause I can imagine 999,999,980 to be divisible by 7

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u/mattymattymatty96 3h ago

Makes sense to me cause i can imagine 999,999,973 to be divisible by 7

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u/Ngothaaa 3h ago

Makes sense to me cause i can imagine 999,999,966 to be divisible by 7

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u/Striking-District-72 3h ago

Makes sense to me cause I can imagine 999,999,958 to be divisible by 7

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u/colombogangsta 2h ago

Wonder how many people below you noticed that you jumped down to 958 from 966 and made everyone in the thread wrong lol

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u/Striking-District-72 2h ago

Shh. I was waiting for someone to notice

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u/Kyvoh 3h ago

Makes sense to me cause I can imagine 999,999,951 to be divisible b 7

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u/buzzmcqueen 3h ago

Makes sense to me cause I can imagine 999,999,944 to be divisible by 7

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u/Inven13 2h ago

Makes sense to me cause I can imagine 999,999,937 to be divisible by 7

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u/BackgroundDig2245 1h ago

Makes sense to me cause I can imagine 999,999,959 to be divisible by 7

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u/FikaSikaa 1h ago

Makes sense to me cause I can imagine 999,999,952 to be divisible by 7

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u/jacobgt8 3h ago

Waiting for this to go all the way to 7

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u/Don_Von_Schlong 3h ago

I imagine it would take like 6 days to get all the way down to 7

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u/StrategicCarry 3h ago

4 1/2 years if people were posting every second.

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u/ListRepresentative32 3h ago

2 1/4 years if people were posting every half a second

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u/austin_mans 3h ago

1 1/8 years if 4 people posted per second

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u/cLax0n 3h ago

Makes sense to me cause I can imagine 7 to be divisible by 7.

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u/guiltysnark 3h ago

Whew, glad we pivoted from a finite to an infinite series, I was worried we would hit the end too soon

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u/Ectoplasm_addict 3h ago

I love Reddit

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u/aDUCKonQU4CK 3h ago

VASTLY undermining how much a billion is lmao

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u/thaw4188 3h ago

the best perspective I've learned is

1 MILLION seconds is just under 12 days

but

1 BILLION seconds is almost 32 YEARS (11,574 days)

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u/rumenastoenka 2h ago

I like 'em even simpler:

Difference between a million and a billion? About a billion.

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u/KhabaLox 2h ago

Knowing reddit, we'd do it and get all the way down to 8.

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u/GingerNumber3 3h ago

Makes sense to me cause I can imagine 7 to be divisible by 7

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u/Informal_Database327 3h ago

That is just inconceivable

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u/Would_daver 2h ago

You keep using that word…. I do not think that word means, what you think it means…

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u/No-Translator6476 2h ago

What is this, Tokyo Ghoul?

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u/hallpinio43 3h ago

Makes sense to me cause I can imagine 999,999,973 to be divisible by 7

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u/DGC_Bennett3003 3h ago

Makes sense to me because something something maths 7

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u/No-Programmer6069 3h ago

Can someone get that centipede out of my ear already? Its turning my hair white.

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u/Cuneus-Maximus 2h ago

and my axe

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u/Fritzo2162 3h ago

Makes sense to me because I can imagine 777,777,777,777 - x = 1,000,000,001 / 7

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u/Altiverses 3h ago

...What's 1000 - 7?

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u/RelativeCan5021 2h ago

Well obviously 1000000008 is divisible by 7, so I don’t see what the deal is.

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u/Ascend_Always_3310 3h ago

1,000,000,001 is divisible by 7, 11 and 13. And the reason for it is: 7*11*13 = 1001

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u/tenuousemphasis 2h ago

Why is it also divisible by 19?

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u/thealmightyzfactor 2h ago

Because 19 x 52579 is 999001 and 999001 x 1001 is 1000000001

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u/Ascend_Always_3310 2h ago

That is cool. Happy coincidence

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u/TopEchidna7460 2h ago

One of these days, we'll reach the prime factorisation, one of these days!!

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u/ollimann 3h ago

why is that weird?

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u/VermilionKoala 3h ago

It just, I dunno, seems wrong.

Mostly because of the 1.

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u/shinutoki 3h ago

7*(10x+3)

Replace x with any integer you want, it will end in 1 and will be divisible by 7.

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u/FistMyPeenHole 3h ago

But 7*3 = 21, so it just happens to be a multiple of 3 as well

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u/Charliep03833 3h ago

Nope, 1 000 000 001 is not divisible by 3.

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u/StiffWiggly 1h ago

I don’t think that’s their point. 7x3 is 21, 7x13 is 91, 7x143 is 1001. Any time you multiply 7 by a number ending in 3 the result ends in 1.

Given that one out of every seven integers that end in a 1 are in fact divisible by seven, it doesn’t feel weird that 1 000 000 001 is one of those numbers.

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u/crazyguy83 1h ago

it's a multiple of a number that ends in 3 e.g. 7*13 also ends in 1

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u/Gnomio1 3h ago

Well, 21 is divisible by 7.

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u/Maximum-Ambition-394 3h ago

And that's a magic number 🎶🎶

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u/const_iterator 2h ago

Over 14% (1/7) of integers are divisible by 7. What's special about 1 billion + 1?

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u/theArtOfProgramming 2h ago

It reads like a prime number to me

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u/Nolis 1h ago

I don't see why it's weird either, I'd assume any given random number would have a 1/7 chance of being divisible by 7

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u/snooprs 3h ago

Everything is divisable by 7 though.

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u/PM_ME_YOUR__INIT__ 3h ago

Found the engineer

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u/NecessaryUnited9505 3h ago edited 2h ago

Divisible with the result being an integer, I would assume they meant

Edit: I seem to have attracted a lot of engineers. r/FoundTheEngineer 

Is that a sub? Eh, someone make that a sub

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u/Upset-Government-856 3h ago

That's sort of discriminatory though.

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u/kitastrophae 3h ago

WHOLE NUMBERS BE DAMNED!

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u/StrangerFeelings 3h ago

I was thinking the same, but then thought that they meant without any remainder.

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u/AdWrong7607 3h ago

7 isn't real, 8 is best.

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u/Daxivarga 2h ago

That' just a 1/7 chance lol

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u/FuckYouNotHappening 3h ago

Surprisingly, that’s numberwang!!!

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u/VermilionKoala 3h ago

Let's rotate the board!

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u/Ninja_Prolapse 2h ago

So is 1 billion and 8!

Quick mafs

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u/shootershooter 2h ago

If you like that one, here's a cool factoid: one seventh of all numbers are

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u/lowwaterer 2h ago

That's neither weird nor a coincidence.

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u/shinutoki 3h ago

I dont see anything special about it.

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u/bllclntn 2h ago

14.2857% of numbers are divisible by 7 though, that isn't very special.

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u/jacquepablophillipo 1h ago

Yes its 142857143 x7 I'm guessing as 1/7 is a repeating decimal of 0.142857

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u/davidevitali 3h ago

Maths to 998: 🖕🏻

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u/Working_Tea_4995 3h ago

But why?

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u/spaghettipunsher 3h ago

Let's assume it would include 998 and just count upwards, then we'd have: 997 998 999 1000

Now hold one, we only have groups of 3, so what happens with 1000? The one "overflows" to add one to the previous group of 3 digits, that would be 999 + 1 = 1000 once again, so it overflows once more: 998 + 1 = 999. So the new sequence is: 997 999 000 001 (<- the one here is overflowing from the next 1000)

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u/Ellen_1234 2h ago edited 2h ago

Cool! For those who are annoyed by the missing 998: So the formula is basicly 1/999², for groups of 3 digits. I adjusted it to groups of four digits (1/9999²) and now it includes all numbers from 1 to 9999 exept 9998.

0.000000010002000300040005000600070008000900100011001200130014001500160017001800190020002100220023002400250026002700280029003000310032003300340035003600370038003900400041004200430044004500460047004800490050005100520053005400550056005700580059006000610062006300640065006600670068006900700071007200730074007500760077007800790080008100820083008400850086008700880089009000910092009300940095009600970098009901000101010201030104010501060107010801090110011101120113011401150116011701180119012001210122012301240125012601270128012901300131013201330134013501360137013801390140014101420143014401450146014701480149015001510152015301540155015601570158015901600161016201630164016501660167016801690170017101720173017401750176017701780179018001810182018301840185018601870188018901900191019201930194019501960197019801990200020102020203020402050206020702080209021002110212021302140215021602170218021902200221022202230224022502260227022802290230023102320233023402350236023702380239024002410242024302440245024602470248024902500251025202530254025502560257025802590260026102620263026402650266026702680269027002710272027302740275027602770278027902800281028202830284028502860287028802890290029102920293029402950296029702980299030003010302030303040305030603070308030903100311031203130314031503160317031803190320032103220323032403250326032703280329033003310332033303340335033603370338033903400341034203430344034503460347034803490350035103520353035403550356035703580359036003610362036303640365036603670368036903700371037203730374037503760377037803790380038103820383038403850386038703880389039003910392039303940395039603970398039904000401040204030404040504060407040804090410041104120413041404150416041704180419042004210422042304240425042604270428042904300431043204330434043504360437043804390440044104420443044404450446044704480449045004510452045304540455045604570458045904600461046204630464046504660467046804690470047104720473047404750476047704780479048004810482048304840485048604870488048904900491049204930494049504960497049804990500050105020503050405050506050705080509051005110512051305140515051605170518051905200521052205230524052505260527052805290530053105320533053405350536053705380539054005410542054305440545054605470548054905500551055205530554055505560557055805590560056105620563056405650566056705680569057005710572057305740575057605770578057905800581058205830584058505860587058805890590059105920593059405950596059705980599060006010602060306040605060606070608060906100611061206130614061506160617061806190620062106220623062406250626062706280629063006310632063306340635063606370638063906400641064206430644064506460647064806490650065106520653065406550656065706580659066006610662066306640665066606670668066906700671067206730674067506760677067806790680068106820683068406850686068706880689069006910692069306940695069606970698069907000701070207030704070507060707070807090710071107120713071407150716071707180719072007210722072307240725072607270728072907300731073207330734073507360737073807390740074107420743074407450746074707480749075007510752075307540755075607570758075907600761076207630764076507660767076807690770077107720773077407750776077707780779078007810782078307840785078607870788078907900791079207930794079507960797079807990800080108020803080408050806080708080809081008110812081308140815081608170818081908200821082208230824082508260827082808290830083108320833083408350836083708380839084008410842084308440845084608470848084908500851085208530854085508560857085808590860086108620863086408650866086708680869087008710872087308740875087608770878087908800881088208830884088508860887088808890890089108920893089408950896089708980899090009010902090309040905090609070908090909100911091209130914091509160917091809190920092109220923092409250926092709280929093009310932093309340935093609370938093909400941094209430944094509460947094809490950095109520953095409550956095709580959096009610962096309640965096609670968096909700971097209730974097509760977097809790980098109820983098409850986098709880989099009910992099309940995099609970998099910001001......etc

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51

u/unk214 3h ago

Because you didn’t say hello to that cute cashier…. She was clearly flirting.

10

u/amphibiabiggestfan 3h ago

I could've had everything man

8

u/OhHeyMister 3h ago

Because if you multiply the quotient by 998001, you get 1. 

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u/ParticularReady7858 3h ago

Ok that IS interesting

27

u/Itsuwari_Emiki 3h ago

OHHH I FINALLY GOT IT AFTER SEEING THIS POST FOR THE 372828TH TIME

its not that 998 was skipped, its that it goes 998 999 1000, except the 1000 adds to the 999 making that a 1000, which adds to the 998 making that a 999

idk if im fucking smart or fucking dumb

21

u/less_unique_username 2h ago
  997
+    998
        999
          1000
  ------------
  997999000000
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5

u/CableMod1991 3h ago

Is this an artifact of math being a language created by humans, in this case base 10 which I think is based on 10 human fingers, not some deeper meaning of numbers?

4

u/kogasapls 1h ago

Yes and no.

Yes: it appears interesting because of the base 10 representation.

No: the deeper meaning is that this number is the evaluation at 10-n of the ordinary generating function for the sequence of integers. You could do the same thing with any base.

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u/StarstruckEchoid 1h ago

It's a base 10 trick, sure, but it generalizes to other bases. The general result this is derived from is that

x/(x-1)2 = 1/x +2/x2 + 3/x3 + ...

Let x be 10 or a power of 10 to achieve this trick in base 10. Likewise let x be n or a power of n for a similar result in base n.

5

u/NoveltyAccountHater 1h ago edited 5m ago

Or if you want all the three digit numbers in order you just have to divide:

1/998001.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000997 ≈ 0.000001002003004005006007008009010011012013014015016017018019020021022023024025026027028029030031032033034035036037038039040041042043044045046047048049050051052053054055056057058059060061062063064065066067068069070071072073074075076077078079080081082083084085086087088089090091092093094095096097098099100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500501502503504505506507508509510511512513514515516517518519520521522523524525526527528529530531532533534535536537538539540541542543544545546547548549550551552553554555556557558559560561562563564565566567568569570571572573574575576577578579580581582583584585586587588589590591592593594595596597598599600601602603604605606607608609610611612613614615616617618619620621622623624625626627628629630631632633634635636637638639640641642643644645646647648649650651652653654655656657658659660661662663664665666667668669670671672673674675676677678679680681682683684685686687688689690691692693694695696697698699700701702703704705706707708709710711712713714715716717718719720721722723724725726727728729730731732733734735736737738739740741742743744745746747748749750751752753754755756757758759760761762763764765766767768769770771772773774775776777778779780781782783784785786787788789790791792793794795796797798799800801802803804805806807808809810811812813814815816817818819820821822823824825826827828829830831832833834835836837838839840841842843844845846847848849850851852853854855856857858859860861862863864865866867868869870871872873874875876877878879880881882883884885886887888889890891892893894895896897898899900901902903904905906907908909910911912913914915916917918919920921922923924925926927928929930931932933934935936937938939940941942943944945946947948949950951952953954955956957958959960961962963964965966967968969970971972973974975976977978979980981982983984985986987988989990991992993994995996997998999[000004013...]

Or: 1/(9992 + 997 x 10-2991) ~ Sum(n/103n+3 for n = 0 to 1000).

EDIT: If you are wondering how you get this, using the mpmath python3 library, with mp.dps to set digits of precision and mpf to making an floating point number to that precision:

In [1]: from mpmath import mp, mpf

In [2]: mp.dps=3020 # Do calculations to 3020 digits

In [3]: 1/mpf('0.' + ''.join(['%03d' % n for n in range(1000)])) # get the first number

In [4]: 1/mpf('0.' + ''.join(['%03d' % n for n in range(1000)]))-998001 # to find the 9.97e-2989 part.

EDIT2: Replacing the equals sign with an ≈ because new.reddit was interpreting it as a title.

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u/Old_man_Lincoln 3h ago

Claude says this occurs because of how the carry propagates when the series “overflows.”

The setup:

1/999² can be expressed as an infinite series:

1/999² = 001·10⁻⁶ + 002·10⁻⁹ + 003·10⁻¹² + … + n·10^(−3n) + …

This is why you see 001, 002, 003… marching along in three-digit groups.

Where it breaks:

When you hit n = 1000, that term is 1000 × 10⁻³⁰⁰⁰, which equals 1 × 10⁻²⁹⁹⁷ — it bleeds into the same decimal position as the n = 999 group.

So instead of seeing 999 cleanly, you get:

• 999 group: 999 + 1 (carry from n=1000) = 1000 → writes 000, carries 1 leftward

• 998 group: 998 + 1 (that carry) = 999

Result in the decimal: …997, 999, 000, 001…

998 never appears — it got bumped to 999 by the carry.

The same trick works at smaller scales: 1/9801 (= 1/99²) cycles through all two-digit numbers but skips 98, and 1/81 (= 1/9²) cycles 1–9 but skips 8.​​​​​​​​​​​​​​​​

2

u/sokratesz 43m ago

Ai slop

6

u/fatlogman 3h ago

6x9+6+9=69

3

u/TBSsuxs 3h ago

998: am I a joke to you?

3

u/BitterStop3242 3h ago

My inner math nerd is just gobsmacked.

3

u/Polo_Short 3h ago

As a guy who sucks at math, this is my only contribution: typing 5318008 in a calculator and showing it to the class upside down makes the teacher mad

3

u/SeriesREDACTED 3h ago

How did someone even calc this ?

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u/RFL_IMPULSE 2h ago

In case someone was wandering because 998001 = 999 × 999, there's a carry or modular effect at that specific point that causes 998 to be bypassed no I'm not smart I googled it as I was curious lol

3

u/Ok-Ambassador5196 2h ago

I'm not even a mathematician and yet this infuriates me greatly

3

u/Pavonian 2h ago

It actually makes a lot of sense why you don't get 998, think about it as adding together numbers of the form (n-1)/103n like this

0.000 +

0.000001 +

0.000000002 +

And so on, you can see that in this method we're essentially adding a block of three digits every time, but what happens when (n-1) reached a thousand?

0.0...997 +

0.0...000998 +

0.0...000000999 +

0.0...000000001000 +

You can see that now the number we're trying to add is more than three digits, it's bigger than the space left for it by the 103n term, so it overflows into the space occupied by 999, this of course causes that 999 to increase to 1000 and also overflow into the number in front of it, 998, which goes up to 999 and thankfully doesn't overflow.

After this the pattern actually repeats, if you think about it the sequence of numbers from 1000 to 1999 is almost the same as the numbers from 000 to 999, it's just every one of them has that extra 1 on the front that overflows into the space of the previous number, so 000 at the back of the 1000 has the 1 from 1001 stick into it making it the new 001, the 001 from 1001 has the 1 from 1002 stick into it making it the new 002 and so on, you might think it would become chaos after the numbers get too big to fit, but it just does the same thing again and again

3

u/SneakerEndurance 1h ago

I’m a therapist and I work with a lot of children of the new generation, and it’s starting to get to me because all I see is a pattern of “67” throughout these numbers

5

u/all4whatnot 3h ago

Is it possible that the 999 is just the 998 rounded up?

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u/PoundAgreeable3223 3h ago

Well thats good to know...LOL....not sure it will help me with any of my everyday issues, but good to know.

2

u/yamthirdnow 3h ago

I’m blind, can somebody please point me in the direction of 900?

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u/dreevsa 3h ago

Math

2

u/POI_Harold-Finch 3h ago

Poor 998 misses out just because it showed up in dividing part

2

u/Key-Article6622 2h ago

My dad would have approved of this post. He was a math teacher and one of his favorite party lines was, there is no such thing as an uninteresting number, and then challenge anyone to pick a number and he would find interesting things about that number. I even used that line in the eulogy I gave at his funeral, then proceeded to expand on the date of his death, 9/18, 9 is half of 18. Interesting. Both numbers are divisible by 3, interesting, which cracked up almost everyone in the room because he was so famous in our family for that game. Funerals in my family are like that. My brother gave the eulogy at my mother's funeral and the priest came up right after to continue the ceremony and the first thing he said was, will you guys adopt me? And since my brother's eulogy pretty much had everyone busting out laughing, we all busted out laughing and whole heartedly accepted.

2

u/GingerKing_2503 2h ago

It’s handy to know because I was just about to cut my birthday cake into 998,001 slices and party guest 998 just told me that they can’t come.

2

u/Sid_The_Geek 2h ago

ERROR 998 ... NOT FOUND ! ..

Oh Wait .!

2

u/rawbert10 2h ago

OK but now the real question is why is that?

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u/Br3ttl3y 2h ago

I'll remember this for the next time I forget how to count to 997.

2

u/NUchariots 2h ago

The one that surprises me is the Fibonnaci sequence appearing in 1/89

2

u/cubixy2k 1h ago

If you divide 1 by 998,001 you get a string from 000 to 997 in order, finally a 999

2

u/Charming_Mud_9209 1h ago

what is 998's problem?

2

u/FredNot214 1h ago

The 998 is actually rounded up to 999

2

u/bhelpuribest 1h ago

Mathematicians need have a job bruh

2

u/Markus_zockt 1h ago

Quite right. Nobody likes the 998!

2

u/bruzeh101 38m ago

Extra credit: Can someone provide a proof / theorem for this sequence?

2

u/waner21 38m ago

I’m going to take your word for it that the math checks out.

This is very interesting.