A Sequence with a Mistake - Numberphile

Sequence guru Neil Sloane on a sequence which puzzled him - until he spotted the mistake!
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[@azdarksonal]

This man was so disgusted by the website's attempt at making his life's work seem vain, that he returned to make a quick video explaining how the quiz itself is an idiot. Amazing.

[@Simon-ph1nf]

sequence that peasant!

[@oofusmcdoofus]

Parry this you casual

[@strateeg32]

what you mean 'returned'?

[@h00db01i]

@@strateeg32 what you mean 'what you mean 'returned''?

[@strateeg32]

@@h00db01i the person who made this post said the guy returned to make a quick video. So i was wondering why he said returned. Did the guy retire?

[@JaccovanSchaik]

On behalf of the Netherlands I'd like to apologise for this egregious mistake. Please be assured we will find the ones responsible, and we will make sure they never make a mistake again.

[@61Ldf]

Pls. confirm you will feather him...

[@ememmeme8722]

@Andrew K Sir, this is Wendy's

[@sofia.eris.bauhaus]

this shameful INSULT TO MATHEMATICS cannot be atoned for by a simple human sacrifice.

[@ricarleite]

How often are mistakes made in the Netherlands?

[@Dec38105]

@@ricarleite its too dark & dont like those zombie pigmen

[@darkrush908]

Plot twist: it wasn't a mistake. Every 4th entry into the sequence requires the operations to be switched and we just haven't seen the 8th entry into the sequence.

[@fenryrtheshaman]

that's not a sequence though

[@DidierLoiseau]

@@fenryrtheshaman why not?

[@highpath4776]

@@DidierLoiseau Because the 85 to the next number does not give the number given.

[@DidierLoiseau]

@@highpath4776 (85+1)×5=430, (430+1)×6=2586, so the rule “add 1 and multiply by the sequence number, except for every 4th entry, for which you swap the operations” still works, and it goes on with 18109, 144873, 1303866, 13038670…

[@inmathswetrust5293]

Then they should give more numbers

[@andr101]

Neil Sloane should narrate audiobooks of tales for children. He has a wonderful voice.

[@dominik.sauer1]

Wasn't it just a typo? 5 n some fonts looks a lot like 8.

[@RebelKeithy]

@@dominik.sauer1 No, because after 88 the next number would be (88 + 1) x 5 = 445 not 430. So the mistake throws off the rest of the sequence.

[@61Ldf]

Niel might

[@dominik.sauer1]

@@RebelKeithy Ok, so maybe sloppily written 88, coffee break, 88 read as 85?

[@h00db01i]

@@dominik.sauer1 why you hijack a comment about his voice? maybe learn how to use forums, bud

[@tormodguldvog8405]

"I'm supposed to be an expert" Neil Sloane FTW @ 81 years old. We need more people with his selfless sense of humor.

[@honorarymancunian7433]

He's 81?!

[@garrick3727]

That is a fairly spectacular mistake. One would think that, given you know you are multiplying by 4 in that step of the sequence, the result should have been an even number. That's the kind of check they teach you in school.

[@garrick3727]

@@StellardroneMusic Go on then, what number did you have in mind that fits the context of this video dealing with integer sequences?

[@josiahfour25]

@@StellardroneMusic Yes, every natural / integer number multiplied by 4 is an even number.

[@KevinVanOrd]

@@StellardroneMusic We're eagerly waiting for your example of a positive integer multiplied by 4 that is an odd number.

[@mathsman5219]

@@KevinVanOrd 😶

[@NoriMori1992]

@@StellardroneMusic Bruh

[@anaghshetty]

He returned when we needed him the most

[@utuber1789]

not the mathematician we deserve, but the one we need!

[@Triantalex]

false.

[@80Mollusc]

Neil Sloane has quickly become one of the GOATs of Numberphile, up there with Matt Parker, Dr. James Grimes, and Alex Bellos!

[@JSLing-vv5go]

He didn't contribute as much to NP, but let's not forget Dr. Conway. What a legend!

[@AliveInTwilight]

Agreed! But this GOAT list must include Hannah Fry too.

[@pataplan]

*Grime (no 's')

[@salerio61]

No Cliff Stoll?

[@dominiczinn8751]

This channel never fails. The sheer joy and wonder in Neil’s voice inspires me to no end

[@cadekachelmeier7251]

It's not a mistake. The "n"th term is given by the equation (47/36)*n^6 - (521/20)*n^5 + (1883/9)*n^4 - (10255/12)*n^3 + (66599/36)*n^2 - (29698/15)*n + 801 I'm surprised you didn't see that.

[@MrDannyDetail]

Having tried that in a spreadsheet, that generates: 53.1, 1669.2, 12666.3, 53371.4, 162897.5, 405559.6 and so on. It's interesting in that it cycles perfectly through all digits in the tenths column in numerical order.

[@R_V_]

_Laughs in Lagrangian_

[@pooqy]

53.1, 1669.2, 12666.3, 53371.4, 162897.5, 405559.6, 878230.7, 1718637.8, 3114597.9, 5314194, 8636891.1

[@tulsiramcommittee6879]

Hi

[@omp199]

After your edit, this is correct. This solution, together with some explanation of what led to it and how the same principles work more generally, would have made for a much more interesting video.

[@Gakulon]

Always love videos with Neil Sloan!

[@GreRe9]

It's series A090805 ("A simple recurrence with one error." in the OEIS.

[@verheggn]

'Cheaters never prosper' - I loved the little Dutch easter egg you put there.

[@LeventK]

When you're almost done with the question but you find the friction negative:

[@DirtyDan16_]

-1/12

[@LeventK]

This reply is genius. @@DirtyDan16_

[@nope110]

Shouldn't friction generally be negative since it acts in the opposite direction to whatever force you're considering?

[@markfox1545]

Friction? More lube. Sorted.

[@vinlebo88]

@@nope110 No, you usually calculate a (positive) friction constant using a formula for a (negative) friction force.

[@ventsislavtsenov4031]

Does Neil Sloane bring his own editor? Haha. The visual style of all numberphile videos with him is so unique

[@Tahgtahv]

I believe that would be the amazing Pete McPartlan. His animations really bring the videos to life and help set apart the various presenters.

[@Triantalex]

??

[@ayshatc]

The sequence also works this way! Fascinating though. The formula is a_(n+1)=(a_n × n) + n a1 = 1 a2 = (1×1) + 1 a3 = (a2×2) + 2 . . . an = (a_(n-1)) + (n-1) Feel free to correct it if it's wrong!

[@SpencerTwiddy]

it is obvious that these are mathematically equivalent: 3*(6+1)=21 : 3*6+3=21 4*(21+1)=88 : 4*21+4=88 etc. it's just one distribution: n*(x+1) = n*x + n your general formula should also be edited though: a_n = a_(n-1)*(n-1) + (n-1)

[@freshpressedify]

You can also do x1+1, x2+2, x3+3 etc.

[@eladidu3]

That's because n*(a+1)=n*a+n

[@nathanderhake839]

0:16 No one is talking about how the coffee shop charges $78 for a coffee.

[@asheep7797]

but what country's dollars?

[@PerFnurt]

Well, a coffee shop in the Netherlands actually isn't really about coffee.

[@carpyet9507]

These videos are like an infinite content well for Numberphile, and I don't mind.

[@paulb7027]

When I saw {1, 2, 6, 21, 85}, I thought the method was #1: multiply by 1, add 1 #2: multiply by 2, add 2 #3: multiply by 3, add 3 ... which is basically the same thing. But of course the mistake still occurs.

[@JoshDavidLevy]

Love seeing this guy again. The Sloane videos are consistently among my favourite Numberphile episodes.

[@howdidthisgethere119]

These sequence puzzles always infurate me. I think it's going to be math, but it's always -Add the numbers of a decimal digit together -count the number of lines needed to draw it with roman numbers -look for the number of holes in the digits -Give the factorial value of the next animal listed after the number alphabetically if all of the letters in the animal's name had a numerical value. Even on math exams in school it'll be "aabbc+adbcc = acefd" Find all of the letters. (the letters are a string of digits, not a sequence of multiplied digits) I was near the top of my class in math, but we never encountered those outside of standardized tests.

[@TheSudsy]

probably how individuals brains work or are wired up. Mathematics is precise and has rules and is logical. The puzzles are a bit of a juxta position to this and probably suite people who can maybe score a high IQ test but not necessarily excel at Maths. Some people like Neil cross over into both states, a quantum Numberphile lol

[@Mnnvint]

@@TheSudsy Sloane dislikes these kinds of puzzles himself, he's said as much earlier. If it's math, you ought to be able to verify for yourself that the answer is correct. But on IQ-test type puzzles (and "determine the next number in the sequence" is a classic example), the goal is virtually always to guess what the task really is, what the guy creating the test meant, and you can never be sure you got that right. Thus, they're more like riddles or secret handshakes than math. Are you in on the secret? Do your thoughts go along the same esoteric directions as we do, so that this makes sense to you? And that's a bit disgusting to claim as the true measure of intelligence.

[@davidconnell1959]

As brief and seemingly insignificant as this is, I’m sure it is my favorite from Prof. Sequence. I will remember this one and its implications.

[@WillToWinvlog]

I'm always happy to see Neil on here!

[@HeyMJ.]

Thank you for a clear demo; solving a ‘number sequencing’ problem’ w/a large paper sheet, colored markers (wide-tip), and a large font. Following along & being ability to apply the method was delightful!

[@Luffy_wastaken]

Please make some videos starring James Grime again...I miss him on numberphile

[@jameslima9817]

I love that the animation has him wearing a Hendrix shirt. Bonus points.

[@siplebrice]

I'm sure it's been said already, but there are a number of ways to interpret the sequence so that the answer is the same. I absolutely love oeis, Neil Sloane, and number sequences in general, I have 2 published on oeis myself! (A25602, A25603) One that springs to mind: multiply by n then add 1 if a(n-1) is odd, add one then multiply by n if a(n-1) is even.

[@robodrew]

Assuming the same mistake, this can also be solved via: (a*b + b) wherein a is a number in the sequence and b is its position in the sequence. But the answer that Dr. Sloane came up with is the answer that perfectly explains the puzzle's mistake!

[@cawasame]

Watching this video I remembered when a former student once called me in despair, because he was trying to implement a computer program found in a magazine, but he always got a wrong result in the program. After trying several times, he called me to ask me if I thought he was a bad student, because if my answer was yes he would drop out of the Information Technology course. I remember the "deadly silence" he made when I asked him back: "But why are you thinking about dropping out of school, just because you can't implement a computer program with a printing error in a magazine ?!" ... The mistake was that somewhere in the program a 5 was printed instead of an S!

[@peterkelley6344]

LOL ROF. Been there. done that! I know the feeling!

[@gunar.kroeger]

I'm so happy I figured it out from the thumbnail, saw that it didn't work, watched the video and I was correct after all

[@mostafabjn2796]

Same

[@entropy730]

Neil Sloane: *appears behind puzzle maker, pushes up glasses* "Nothin' personal, kid."

[@glowstonelovepad9294]

1, 2, 6, 21, 88, 445, 2676, 18739, 149920, 1349289, 13492900 are the first 11 terms of the sequence.

[@omp199]

I prefer the sequence 1, 2, 6, 21, 85, 430, 2586, 11425, 38145, 104194, 246134, ... It fits the question better. :)

[@notcoachfou7841]

Multiplying by the number in the sequence and then adding that same number also works. 1*1+1=2 2*2+2=6 6*3+3=21 21*4+4=88 Using incorrect value: 85*5+5=430 430*6+6=2586

[@aledandrian]

The Parker Sequence

[@mienzillaz]

For sure;)

[@mirador698]

I was looking for this comment 😂

[@evanhawkins6073]

I figured this one out pretty quickly. I noticed the pattern with the first 4 in the sequence and realized the multiplier value kept climbing by 1. So, based on that, I divided 2586 by 6 and subtracted 1. When you take 430 then divide by 5 and subtract 1 you get 85. Based on the way I approached it I never got hung up on the continuity of the sequence. If you try to follow the progression further in reverse the sequence breaks because you’ll get 21.25. So, the order of operation flips at the 5th number in the sequence. I see the professor’s point, but I think this sequence forces you to think beyond the limits of the number of clues in the sequence if every 5th entry requires a flipping of operation sequence. I was able to solve what an expert wasn’t. I may put this sequence on my gravestone. 😊

[@wallywutsizface6346]

This is the first one of these I’ve ever figured out on my own

[@Danscottmusic]

It's not a mistake, every 4 numbers you swap the order of operations

[@secularmonk5176]

EXCELLENT RETORT (reminds me of the rules for the Gregorian calendar)

[@peace2652]

Neil Sloane is a legend.

[@Posiadam.]

The more intuitive method in my opinion would be this one: 1 -> 2 (multiply by 1, add 1), 2 -> 6 (multiply by 2, add 2), 6 -> 21 (multiply by 3, add 3). That’s how I figured it out. Maybe if the people behind the puzzle had figured out this way there wouldn’t be this huge mistake. Moreover you can check it fairly easily, if you multiply something by 4 you always get an even number, not 85 🤦‍♂️

[@mossworksmedia]

It looks like it could have also been a transcription error on 10-key as 5 and 8 are right next to each other, which is fascinating to me that these two types of errors produce the same result, or rather that a typo yields the same result as swapping the order the operations are performed

[@highpath4776]

Oh my, sequences based around errors where there is a real pattern but the randomness of the answer each time being mistyped in itself a particular sequence would be quite challenging.

[@vsm1456]

@@highpath4776 sounds pretty unique!

[@pskelly56]

I'd like to know why, on the bookshelf behind him, he has the books' spines turned away and the topic of the book written on the bottom edges of the pages.

[@TheBurningWarrior]

To minimize space requirements. He can't fit them all on the shelf, so he's stacking them sideways to minimize their footprint.

[@glowingfish]

And he has to write the topics so he knows what book it is.

[@Dhoing]

Awesome! More of him pls 😊

[@thememeestfilmbuff]

*They made this as a puzzle,* but I feel like a lot of people don’t even notice how it’s wrong. _It’s like how some people think that 2 + 2 equals fish._

[@3ckitani]

What do you mean 2 + 2 is clearly equals fish

[@cptazstudios7952]

It’s common sense that 2+2=fish

[@bradleyparrett4483]

Instead of +1 ×1; +1 ×2; +1 ×3 etc this pattern also works with ×1 +1; ×2 +2; ×3 +3 etc. To get 85 you accidentally add 1 instead of 4.

[@aekhoury98]

nX + n = n(X + 1).. it's the same formula

[@uelssom]

Cant wait for the next video of Voorwerpivity with Van Kjth

[@ReynaSingh]

This could’ve been avoided if the sequence was longer

[@lucky-ro732]

Yeah, it might make sense if it was like this, after 3 sequence, the 4th one become multiplication first before adding the one so the 5,6,7 all still +1 then multiply by n but the 8th would be multiply by n before +1 if you know what I mean.

[@Keyboardje]

Exactly. But that might have been part of the (intended and misleading) extra difficulty of the puzzle. So you have to not only take in account the given sequense, but also immagine the possible further sequence numbers to catch the true sequence, with every fourth being multiply +1 instead of +1 and then multiply. :)

[@SquirrelASMR]

More videos of him pls

[@bowtangey6830]

Neil: Thank you for your beautiful OEIS.

[@Megamegalomane92]

"now you stare at the sequence, and immediatly see that it must be the values of P(n), where N=1,2,3,4,5,... , and P is the polynomial that interpolates the various values in the sequence, so P(1)=1, P(2)=2, P(3)=6, P(4)=21, P(5)=85, P(6)=?, P(7)=2586. By the theorems about polynomial interpolation there exists one and only one polynomial P of minimum degree lower or equal to 7-1=6 (because we have 7 points to interpolate) that interpolates these points. So clearly the sequence is P(n), where P is this specific polynomial. Conveniently there exists a P with these properties for any value of the uknown point P(6), so pick up your favourite value of P(6) (maybe P(6)=pi) and you get the function P which induces the sequence and can compute P(6)= the value you chose, so the value you chose is the correct answer, for any value you can choose in this way." And this is why I completely hate this kind of question. The question "complete the sequence" is a not a clear question, it is based over the subjective definition of "correct logic", "simplest logic" and whatever else. It's like asking "compute the operation between two numbers A and B, but I am not going to tell you which operation it is. Oh you did A+B? too bad, it was A*B instead." In my opinion that question would be interesting if you added a rule that defines a univocal correct answer, instead of being just based on either a guessing game or a subjective definition of "simplest logic", which is different from person to person.

[@FloydMaxwell]

Sequences on exams are one of my pet peeves. Frequently there are not enough sequence numbers to determine a unique answer, but the person marking the quiz expects only one right answer. Here there are enough numbers -- 1, 2, 6, 21, 85, ?, 2586 -- to catch even an error. Either have enough numbers, or don't put these on exam papers.

[@cityuser]

1, 2, 4, x Is it +1, +2, +3... meaning x = 7 or powers of 2 meaning x = 8? We will never know, we can never know

[@ligmoes]

@@cityuser This. Like others suggested every 4 steps there's a change so it needs a more complex equation to solve. Likewise a sudoku printed on newspapers only give one answer and even tho everyone knows sudokus can have multiple answers, the 'right' answer isn't always the only right answer. Maybe they'll read the comments and look into the extended sequence. Some puzzle makers like to come up with real deep and long solutions that at some point say more about them than the person solving, which becomes trying to social engineer it (study the puzzle maker and how they think) rather than applying logic.

[@robertschlesinger1342]

Interesting and worthwhile video.

[@JohnDlugosz]

The difference in 85 is simply part of a larger pattern; a higher order derivative if you like. You do process A three times, then do B, then do A 4 times, then do B twice, etc.

[@cubesquared2291]

He sounds like Professor Hubert J. Farnsworth (the old guy in Futurama) and it's awesome!

[@FilleMazendacus]

I solved this a bit differently (sorry my bad english).. If we assume that this is a steadily increasing sequence (that is, there are no regressive steps in between), x can be equal to 267 and 586, or anything in between. If we assume that the missing number is 430, then we have the following sequence: 1, 2, 6, 21, 85, 430, 2586 If we look at the difference of each of the following members with the previous member, we get a new sequence: 1, 4, 15, 64, 345, 2156 If we do the same now with this sequence and also with the new sequences obtained, we get 5 more sequences with the same methodology: 3, 11, 49, 281, 1811 8, 38, 232, 1530 30, 194, 1298 164, 1104 940 This 940 is, so to speak, a support-difference that is going to remain constant all the time - it allows us to derive backwards the following member of a given base sequence, which should come after 2586: 1, 2, 6, 21, 85, 430, 2586, 11425 1, 4, 15, 64, 345, 2156, 8839 3, 11, 49, 281, 1811, 6683 8, 38, 232, 1530, 4872 30, 194, 1298, 3342 164, 1104, 2044 940, 940 So, next member should be 11425..

[@R2Cv1]

So sad that he didn't include the Dutch website- presumably because it would get the Hug of Death, but still :(

[@JMDinOKC]

He would be the perfect reader for Spike Milligan's poems for children. "There are holes in the sky where the rain gets in, but the holes are quite small; that's why rain is thin."

[@samstep4279]

The challenge now is to find a rule that gives the sequence including 85. Easy to do, but not a 'neat' rule. What makes a rule 'neat'? (e.g. "for k-th member, add 1, multiply by k, unless k is perfect square, in which case multiply by k and add one". Not neat at all. Is there a neater one?)

[@manuelapollo7988]

I prefer it written like this🙂 1×1+1=2 2×2+2=6 6×3+3=21 21×4+4=88

[@cocacraesh]

I mean what if the sequence is supposed to have addition and multiplication swapped every four steps?

[@gunnarross6321]

Happy to be here so soon.

[@splendidteaching]

I paused the video and thought about it for longer than probably should have. I did come up with a way to generate a pattern with the 85 in place. The missing number, 6th term, I got was 516. Shocked when I played video and saw 430. Anyhow, for those that want to really challenge themselves. The sequence I came up with goes 1, 2, 6, 21, 85, 516, 2586, 11470, 47883 .....It's definately a pattern to the sequence but not easy to discover!

[@MikedeKokkie]

As a Dutch person I am very ashamed for this mistake of my fellow countryman.

[@Konomi_io]

the answer is 1 and the function for the sequence is f(x) = 1757/360*x^6 - 1047/10*x^5 + 31985/36*x^4 - 45433/12*x^3 + 3045653/360*x^2 - 555943/60*x + 3804

[@MrDannyDetail]

Wow! I just tried that in a spreadsheet and the formula you've just said: f(x) = 1757/360*x^6 - 1047/10*x^5 + 31985/36*x^4 - 45433/12*x^3 + 3045653/360*x^2 - 555943/60*x + 3804 actually works for all the given terms and for the blank being 1. Consider me impressed.

[@MrDannyDetail]

Albeit slightly less impressed now that I've realised you were are also the other person I commented under whose formula didn't work (unless I managed to enter it wrongly in my spreadsheet implementation).

[@Konomi_io]

@@MrDannyDetail yeah, i wrote a crappy python script to calculate the given polynomial formula for a given sequence like a year or so ago and i thought this was the perfect time to use it

[@DrMcFly28]

And so the author of the sequence quiz spent the rest of his life in destitute, shamed and forgotten.

[@RobertHartleyGM]

0:11 I genuinely heard "It combines two of my interests: Eric erection and sequences." And I had to pause and think about what else it could have been.

[@skakdosmer]

Ha! I figured it out without having seen the video or the answer first. I saw the pattern from 1 to 2 to 6 to 21 and realised the mistake you’d have to make to get to 85, but of course I wasn’t sure of the pattern I’d found. But then I used the pattern backwards from 2586 and got 430 and 85. It’s always fun when once in a while you manage to be smarter than the teacher, but of course I was helped a little by Brady’s spoiler headline “a sequence with a mistake”.

[@mubarakzain6041]

Wow, I thought that too but after seeing 85 I thought I was wrong.

[@julianrobinson4388]

i get so hyped when i see a neil video

[@shiina_mahiru_9067]

"To identify various things, looks like some kind of a thing" The creativity of mathematicians on coming up with a new word, at its finest

[@chaoslab]

You are such a treasure Neil.

[@bemusedindian8571]

Menu on the wall ;)

[@RupertBruce]

The mistake was merely transcription error - it was written as 88 but was transcribed as 85

[@BangsarRia]

Interesting - being told in the thumbnail that one of the numbers is wrong makes it trivial - even without watching the video - I figured out the algorithm in a few seconds and it took another 20 to verify. Hmmm. You are told there is a mistake, not that ONE of the numbers is wrong, and that actually leads to THREE of the numbers being wrong; the last three. It's a nice twist that the answer to the puzzle is a number that is wrong.

[@splendidteaching]

Also thought I would add a hint if anyone wants to try and work out the sequence 1, 2, 6, 21, 85, 516, 2586, 11470, 47883.... Often for challenging sequences I like to think of how that sequence maps/relates to base 2, ie binary representation. The simplest "landmarks" are with one bit in various positions, ie 2^n. The numbers in this sequence will be between incremental ranges of this. The method I then used was to see how far away this was from a previous landmark and how much to get to the next one. Then mapped a pattern to these differences involving a repeating pattern of a remainder left over after a division. It was this remainder that repeated itself and thus was a "key" to one way of producing this pattern. This is also an interesting technique that I have applied to the collatz sequence and gilbreath conjecture. Life gets in the way of pondering maths for me but if either of these areas are of interest to you I would encourage you to think of number theory problems/puzzles in terms of the structure of the underlying information. Various measures of info complexity ("entropy") can be created and in the case of the collatz sequence can be seen to "drive it". Bit like 2nd law of thermo in physics. Just like modelling nature the math process is just doing what it is doing but in defining an algorithm/equation for info complexity we can see how a process is evolving by how the measure of complexity is changing. Oh well, I am off on tangents again!

[@thomasdupont1346]

The sequence could also have been. 1X1=1 1+1=2 then it's 2x2=4 4+2=6 then it's 6x3=18 18+3=21 then it's 21x4=84 84+4=88, etc. From there on the answers are incorrect since the step to get 85 was done incorrectly in the first place. I believe they might have just done their math wrong on that step as I nearly did since I was rushing and put 21x4=81. 81+4=85. After I looked at that I realized that it was nearly 2am my time and I should probably go to bed instead of trying to do arithmetic, I corrected it to 21x4=84. 84+4=88. My thought is that both the multiplication and addition values increase by 1 with each iteration. 1x1+1=2, 2x2+2=6, 6x3+3=21, 21x4+4=88 and that's where it broke down since they put it at 85 instead, but if we continue using 85 as the next number... 85x5+5=430, 430x6+6=2586, etc. I personally think this is a more elegant way to write it out, but that's just me. And now I'm off to bed before I make any more mistakes than I already have.

[@lordbaysel3135]

It isn't a mistake, just a sequence that is more complicated.

[@spacemanspiff2137]

It’d be funny if the sequence actually used a much more sophisticated algorithm and got it right

[@QuantumHistorian]

For *any* sequence of length n you can find a polynomial of degree n that matches it exactly. That's why these kind of puzzles are meaningless, unless they have a very simple rule which everyone agrees is the 'natural' solution.

[@3ckitani]

@@QuantumHistorian Well the question becomes "How do you figure out the pattern *without* using polynomials?"

[@QuantumHistorian]

@@3ckitani Well then you would rarely be able to. "Add one then multiply by n" can be expressed as polynomial. Any decently well behaved function can be written as an (infinite) polynomial.

[@omp199]

@@3ckitani That doesn't help. There's nothing particularly special about polynomials, here. There are an infinite number of curves that you can draw through any finite number of points. You have to understand that questions like this are not mathematical questions at all, but purely psychological ones: "Guess what the question-setter had in mind when setting this question."

[@splendidteaching]

@@QuantumHistorian Very true. Becomes a bit like like a "halting problem" then as in which do we decide is the most efficient and elegant algorithm....but never quite knowing if something more elegant may be put forth.

[@hannahbrennan7079]

This is the earliest I’ve ever been here! Only 1 minute after posting!

[@joshyman221]

you add 1 to current number and multiply by n (85+1)*5=430.

[@ianwalker6546]

So the sequence is possibly: F(n+1) = 0 when n=0; (F(n) x n +1 when n is a perfect square; (F(n) + 1) x n otherwise, and continues: 1, 2, 6, 21, 85, 430, 2586, 18109, 144880, 1303921, 13039220, 143431431, 1721177184, 22375303405, 313254247684, 4698813715275

[@AgentM124]

G E K O L O N I S E E R D Obligatory comment as a member of the Dutch community.

[@Petertronic]

The highest I could go in the sequence, with a quick program I wrote, is 171 numbers, the 171st being 2.69851166*10^307.

[@salazar4614]

HE'S BACK

[@I_am_Alan]

i like this video very much!

[@CrashDy]

Cool to see some dutch stuff the day before my birthday.

[@gertebert]

Alvast gefeliciteerd!

[@MATHSEXPLORER1]

Sir, how to solve this series problem: 5,7,17,55,225,1131, x , 47559 Find the value of x??? Sir, make the video on this topic please. 👍👍🙏🙏

[@kingshiva5427]

Yes, I also don't figure it out the explicit formula for this.

[@abhishekdevkota8875]

Interesting question 👍

[@Employment613]

6793 donnit erase I didnt show how

[@JBLewis]

I'm forever curious about *which* Mathematica book is in the stack behind Neil.

[@coloneldookie7222]

When the numbers surrounding the function you're trying to solve for, that makes it hard. Had a mistake been made much later, it would have not been an issue. Because if you manage to use the right sequence and correct their error, your answer is right but it won't match their answer.

[@MATHSEXPLORER1]

Sir, how to solve this series problem: 5,7,17,55,225,1131, x , 47559 Find the value of x??? Sir, make the video on this topic please.

[@LeventK]

Interesting question

[@kingshiva5427]

Yes, I also don't figure it out the explicit formula for this.

[@abhishekdevkota8875]

Interesting question 👍

[@kingshiva5427]

@@beel94-de This way is correct but we want know about the unique formula about this sequence

[@kingshiva5427]

Just like we know; 1+1=2 2+1=3 3+1=4 ... ... ... But the unique formula is 👇👇👇👇👇👇👇👇👇👇 1+2+3+4+5+6... +n = n(n+1)/2

[@bowtangey6830]

You probably know this "joke". Einstein was asked by a teacher what number comes next in this sequence: 0, 0, 0, 0, ?, . . . The teacher of course expected the answer to be "zero." But Einstein answered, "24". (If you don't know what pattern would make that answer correct, think about it.) You can use the pattern (assuming you find the one I am thinking of) as the basis for a proof that for any finite string of numbers a1, . . ., an, and any number b whatsoever, there is a simply defined algebraic function f with f(1) = a1, . . . , f(n) = an, and f(n+1) = b. (This bothered me when I took the Postal Exam back in my 20s, as they had such what's-the-next-number questions on it.)

[@kelvinella]

The puzzle is right, it could be any number. For example, it could be 0. Let s(x) = 1757/360*x^6 - 314/3*x^5 + 31961/36*x^4 - 45373/12*x^3 + 3039413/360*x^2 - 36955/4*x + 3790, then s(1) = 1, s(2) = 3, s(3) = 6, s(4) = 21, s(5) = 85, s(6) = 0, s(7) = 2586. DONE.

[@rmagalhaess]

🇧🇷 greetings from brazil! could you say why you have these two books: "Brazil 1" and "Brazil 2" ? (at 1:05, first pile of books) thanks! and Great Video!!

[@JobvanderZwan]

"Voorwerp" Actually, why do we use "pre-throw" to mean "object" in Dutch? That makes no sense (because that's what "voorwerp" literally states)

[@tipeg8841]

Apparently it's a translation of the latin "objectum" (I guess jectum has to do with throwing like the French word "jeter")

[@MonsieurHonHon]

yes more Sloane!

[@SnoopyDoofie]

Plot twist: It's not a mistake. It's the quirkiness of quantum physic's uncertainty principle.

[@ollllj]

There is no mistake. any number sequence is 100% arbitiary, and you can make any number fit. As far as FourierAnalysis is concerned, any number sequence is equally true. The best number-sequence is a costasArray, for being pattern-free, patterns accumulate easier than canceling out.

[@rafaelnfig]

It might have been a typo. Number 5 is next to 8 in the numpad.

[@Trias805]

Is it possible that there's some super complicated formula that gives this pattern?

[@AHBelt]

Yes, you could do what I think Cade Kachelmeier did upthread, which is make a sufficiently complicated polynomial, or you could make the switching the order of the operations on the fifth term, or every fifth term, the new rule, which I was going to suggest.

[@esquilax5563]

For any finite sequence a_n, there is a polynomial p such that p(n) = a_n. So, you can always find a mathsy-looking answer that gives you any next number you want. Once you know this trick though, it stops being interesting

[@yashrawat9409]

These many wrong questions is a standard in exams that include MAT in IN