Brady: what do we know about this sequence? Neil Sloane: nothing. Brady: great! Let's make a video about it!

This man is a legend. I could listen to him talk about numbers forever

"boy, that's a really great sequence" my favourite kind of person

"Boy, that's a really great sequence!"

"X to Z" mathematicians favourite drug

Ok, so after digging a little bit in the sequence, I wanted to share a bit of what I’ve found. I started having in mind to stop when the numbers from 1 to 10 would have appeared but it took me a bit longer than I thought. I finally got a bit further and got the first 252 numbers of the sequence. (I’ve done this on paper, no programming, so it’s possible I failed it at some point) Here are the 56 numbers that appeared in order : 0, 1, 2, 6, 5, 4, 3, 9, 14, 15, 17, 11, 8, 42, 20, 32, 18, 7, 31, 33, 56, 19, 37, 46, 23, 21, 25, 52, 13, 62, 40, 36, 16, 27, 10, 92, 51, 131, 39, 12, 44, 34, 97, 72, 41, 78, 24, 105, 107, 167, 61, 26, 22, 127, 28 and 29. One thing that I found funny with this sequence is that is has the tendency to quickly come back to a number that newly appeared. For exemple when the 9 shows up for the first time, it takes only 3 steps to appear again. Same for 7 and 31. 5, 6, 18 are taking 5 steps to appear a 2nd time, 107 takes 28 steps, etc. But it doesn’t happen for every number, like for 14 that takes 131 steps to appear a 2nd time, but takes 4 steps to appear a 3rd time. ^^ 17 didn’t appear a second time for me even though it comes pretty early in the sequence. It’s hard to find coherence in there but it’s strange to see more often that not new numbers reappearing pretty quickly even though there are still lot of numbers that haven’t appeared yet. The second thing that surprise me a bit is the frequency of new numbers appearing, only takes about 4,5 steps (the longest chain of numbers between two 0s I’ve found is 8 numbers long (found it 2 times)) Thought it would take a bit longer but it’s pretty rare that a new number takes more than 6 steps to appear. But like I said, I only checked the 250 first numbers so I don’t know if it grows up, shrinks or stay pretty much the same if you go further and further. I usually don’t really dig into that kind of stuff, mostly I listen to the video and continue my way elsewhere, but this time my curiosity hasn’t been fulfilled enough, so here I am writing this :p It was worth the try. Thanks Numberphile o/

Numberphile: Don't know Me: * Gets spooked *

- Did you do anything fun this weekend? - Yeah - Yeah? What? - 5:42

I just realized that adding 0 as the next term when there's a number you haven't seen before, isn't as arbitrary as I first thought: It's really just in agreement with the rule of writing down "how far back it occurred last time". When it's never occurred before, the last time it occurred was _right now,_ zero steps ago, so we add a zero. Awesome :D

2:58 now that's some genuine enthusiasm, love it.

One thing that can be proven about the sequence is that VE(n) < n for n > 0 (since the entire sequence has length n+1, the most number of moves back it could take is n, but VE(0)=0 and VE(1)=0, so you'll never go all the way back to VE(0) and thus VE(n) < n). So yeah, f(n) = n seems like a fairly good approximation of the growth of the sequence, but it is also an absolute upper bound on the sequence.

"oooh that's a really great sequince, let me analyze it before anyone else does" I'm gonna go with things only a mathematician would say for 500

This is my new favorite sequence. I love self-descriptive sequences.

Dr Sloane has such a relaxing voice and his love for sequences just radiates from him.

'Oh come on! How can you not know how fast it grows? Surely that's easy to prove! We just... okay maybe we.... what if....' *Three hours later* 'Alright, you win this round...'

Love Neil Sloane videos on Numberphile. Non convential maths at its very best.

Anyone here from advent of code?

I feel like this is another video which is going to inspire a person to “solve” this sequence.

I love these self-referencing number sequences. Reminds me of the Kolakoski sequence.

I love it when Sloane is on the channel. His database inspired me to choose a maths major. I'm so excited for it!!

This is brilliant, it's so simple to think up, yet it's not been submitted before and so unpredictable. I really enjoyed this sequence.

There's extra footage, right? _Please_ tell me there's extra footage.

This is fascinating- it reminds me of John Conway's Look-&-Say Sequence.

I would change the definition of Van Eck's sequence. The sequence doesn't begin from 0 necessarily. Then it is only 0-sequence but it can be N-sequence as well. Then the Van Eck's sequence family was created.

Please keep us updated on this sequence, this is fascinating.

I have watched this video a few times now and absolutely enjoy this video! This is now one of my favorite sequences, it's so delightful! 😀

he always reminds me of Professor Farnsworth. I love it!

I love this guys enthusiasm. Explaining a sequence with a totally unrelated poem. Love it!!

Sloane is so relaxing to listen to.

Another great video. Thanks for producing this extremely engaging material.

I love this sequence, everytime I think it's going to repeat itself it doesn't.

So I saw the title and clicked on the video, and I just glanced at the description for maybe a few hundred milliseconds, and I saw OEIS mentioned, and I thought "oh, nice, they've got the Sloane's entry for it." Then I watched the video and realized that they've also got *Sloane.* :-D

This guy is great. Love his enthusiasm.

I could listen to him listing the sequence like he did in the first minute for hours

Love this guy’s explanations

Another great video enhanced by your very effective animations 👍

this is a super cool sequence, I hope one day someone else wants to talk to this channel about discoveries made about it!

I guess there will never be an end to learning about these number sequences that make me think "well I could have thought of that"

This channel is the channel which aided me to do very well in Mathematics, and is the channel responsible for my uprising interest in this subject!

Fascinating! I have never seen anything quite like this before!

Bless this man

just awesome sequence!!

Would definitely like to see if there's any progress on this sequence

@7:06 4 ways. specifically (+,+,+,+), (+,-,+,+), (-,+,-,-) (-,-,-,-) I found this by the following logic chain: 1. 81 is already divisible by 3, therefore we only need to manipulate the pluses and minuses to preserve this property. 2. 9 is also divisible by 3, therefore it doesn't matter if it is added or subtracted, it will not change the remainder after division by 3. 3. 31, 13 and 4 are each numbers of the form 3x+1, therefore for the purposes of determining whether their sum will be divisible by 3, we need only concern ourselves with the '1' part. 4. the only way to add or subtract 3 1s to each other in any combination and end up with a number that is divisible by 3 is if either all of them are subtracted (-1-1-1=-3) or all of them are added (1+1+1=3), therefore, the first, third and fourth sign must match each other. 5. (4) combined with (2) implies that the second sign can be either plus or minus and the remaining ones must match each other but be either plus or minus and any such combination will work, this means we have 2*2=4 combinations

Listen to this sequence in the library, it is amazing.

There is something so calming about the way he basks in these sequences.

Neil: The obvious questions are… Me: What set of circumstance led to someone creating such an arbitrary set of rules.

2:40 when your crush sends you their bionicle collection

Answer to the daily challenge problem: 4. It is a modular arithmetic question. 81 is divisible by 3 and so is 9. The other numbers each are divisible by 3 with a remainder of 1. All three of those must have either a plus or minus sign. But it must be the same sign for all three. Then thr nine can take a plus or minus and it is independent of the other one. So you have 2 independent choices with 2 options each. 2x2=4.

MOAR OF THIS GUY PLS

the slope roughly equalling 1 is kinda blowing my mind.

Just saw this pop up on the feed. Nice watch

Geez, I love these videos.

Yay, New video!

I could sit and watch an animation showing each number getting added and counting the spaces back for ages, it's hypnotic and pleasing

Numberphile is my favourite channel

I agree very fun sequence. Great upload.

I love you neil sloane for oeis, it is very handy for an amateurish mathematician like me

so lovely

This series is amazing. Not intuitive, sort of alternating and unsolved. Reminds me of the 3n+1 problem, but in a more interesting and (probably also easier to solve) way

Definitely want to see more on this sequence

Hello advent of code folks :)

Brilliant question: Mod 3, the question is: 0 ( ) 1 ( ) 0 ( ) 1 ( ) 1 Where ( ) should be + or -. The maximum value of the expression is 3 and the minimum is -3, occurring when all the signs are + and - respectively (except for the sign before the 0, which can be either). This yields 2×2=4 possibilities. 0 cannot be achieved since the parity of the expression must be odd.

Amazing!!!!!!

Lovely!

Neil Sloane is the piper at the gates of dawn.

That is a great sequence.

Awesome!

Intriguing! Had to write a function in excel for the Van Eck sequence, it sure was fun!

2:15 accidental poetry by Neil Sloane

This was a fun programming challenge. Created an algorithm to compute n values in linear time!

The animation at 2:47 is pure magic. Also, YES, love this guy.

MOAR NEIL

He's the best!

me clicking on a video about sequences: :) Me seeing its neil sloane: :D I just admire him so much!

This man is an excellent teller.

I saw “sequence” and knew it would be Neil!

Brilliant sequence

That is such a poetic sequence.

we want more of neil!

I'm going to answer on a new comment, cause I find the answer interesting by itself, to someone who remarked that if the sequence started with 1,1,... then the sequence would be periodic. The statement is true, but with this set of rules, the first number determines the sequence, and 1,1 is not a valid start for a sequence. In other words, all sequences generated with this rule start by x,0,... . However, we can actually verify that there are at least 2 such sequences that are "profoundly" different (i.e. one is not a subsequence of the other): 0,0,1,0,2,0,2,2,1,... and 1,0,0,1,3,0,3,2,0,3,3,1,8,0,... ("0,0" is a subsequence that appears exactly once on each sequence). A "not profoundly different" sequence would be: -1,0,0,1,0,2,... , if we allow for x to be a negative integer. With this I just realized that if 0,0,... does take all the positive integer values, then it might be "easy" to prove that x,0,... is a "profoundly different" sequence from y,0,... iff x!=y and both are natural numbers. Looking at it in the other way, if there's a value z that's not part of the sequence 0,0,... , then z,0,... is not "profoundly different" from 0,0,... .

AOC 2020 day15.

Ohh gosh, that's an amazing sequence!And there are lots of questions rising: Does the sequence has infinite non zero terms? how often does each term appear? Does each positive integer appear in there? Can we find an algebraic expression for it? In order to find the n-th term, do we really need to know all the previous terms? So many questions, i love it!

Neil Sloan playlist!

We also know that the nth number cant be larger than n, because there arent more than n steps before n. Therefore the fastest way for the sequence to grow is linearly. it could still be root of n or log n, but n^2 or 2^n are ruled out.

I wish my maths teacher was as enthusiastic about maths as he is.

I don't understand this video at all but keep up the great work!

One day I will post a sequence to the OEIS, and Neil Sloane will comment it in Numberphile, and I will be so proud of it. :)

I love simplicity of this sequence.

mind blowing sequence !!! I think it will be very interesting to study the number of zeros in the first "n" terms of the sequence because that is the only number which we can say surely occur or the longest interval in which no zeroes will be there.

Neil's back!

Love the sequence, Love the proof, Love the Pink Floyd shirt!!

Sequence: Boring, boring, boring, ohmygoodnesswhathappenedthere

I wish I had as much enthusiasm as this guy explaining math

I feel that this sequence and its name could be made into a book in the writing style of Dr.Seuss.

Surprisingly interesting.

I love numbers and how they relate with each other. I never heard of this. Has anyone ever programmed a computer to see how far you can go? What I am fond of saying is, "The more I learn, the less I don't know!" (Or realize I don't know.)

Don't know ♥

The less that is known about a sequence the happier Neil is. 🙂

Van Eck: You know nothing, Neil Sloane XD