Don't Know (the Van Eck Sequence) - Numberphile

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Afraid So is by Jeanne Marie Beaumont

NUMBERPHILE

Videos by Brady Haran
Editing and animation by Pete McPartlan

[alexismandelias]

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

[JM-usfr]

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

[robmckennie]

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

[DrMcCoy]

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

[GravelLeft]

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

[julbarrier]

"X to Z" mathematicians favourite drug

[hamfeldt]

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

[gazorpalse]

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/

[shinyeontae]

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

[colinstu]

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

[smileyp]

"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

[GalaxyGal-]

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

[edeleththenerd]

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.

[PopeGoliath]

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

[Calypso]

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

[SunayH]

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

[patrickgono]

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

[AalbertTorsius]

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

[jovi_al]

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

[garethdean]

'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...'