Name: Don't Know (The Van Eck Sequence) - Numberphile (Don't Know (the Van Eck Sequence) - Numberphile)
Uploaded: 2021-01-14T10:16:04.000Z
Duration: 8 min 7 s
Description: VoiceTubeの動画で発音を聞きながら英語表現を覚えよう！学べる英語：

命令形

When you see a new number, the next term is zero.

So we saw a zero, but it was the 1st 1 So the next term is era.

And when you've seen the number before, the next term is how far back?

So we saw it One step back said the next term is one.

So we get a zero and we have seen a zero before.

It was two steps ago and we have seen a two before.

So we get another two and we have seen a two before.

Now, for the first time, something really interesting is happening.

We have seen a one before, but it was 123456 steps back.

Well, we've seen a zero before and it was 12345 steps back.

We keep asking the same questions over and over again.

And this room always reminds me of a poem by Gene Beaumont, which is called Afraid so.

The title is afraid So I was thinking There's so many questions.

So the poem here would be called Don't know What's the next time?

There's every number appear when someone just comes up with a court sequence like this and there's all these.

Don't knows who's drop, is it to find out What is it?

Well, this is one of the great things about being an editor of the Oh, yes, this sequence came in.

It was a submission on one of the pleasures.

The editors don't get paid, but they do get to see these sequences when they come in for the first time.

And so you look at him, you say, Boy, that's a really great sequence.

I'm gonna analyze that before somebody else does.

Why is this one make you smile like that?

Well, partly because it's it's really quite unpredictable.

And so, of course, one of the first things you D'oh!

If you look at the graph, let me see if I can give you a sketch.

So there's zero and zero and a one and zero and two.

It goes and it drops down to zero and it grows and so on.

And if you look at a lot of terms intends to look a bit like this if you close your eyes and squint, if sort of fills up the whole try, and it seems that it's growing about linearly.

If you look at this line, goes through the top, it seems to have Slope one.

But we can't prove that has fun of the many things we can't prove about this.

It could be that after a while we don't see any new numbers.

If the maximum number that ever appeared was 100 then after we seen 100 will be any more zeros because there won't be any more new numbers.

Or maybe it's a 1,000,000 which is the maximum number that appears ever in this sequence.

Now, what that would mean is, since the sequence is defined by how far back you look for the last term, that if the miss number is, say, 100 we would never have to look back more than 100 terms in order to know the complete history.

From that point on, everything would be determined.

But then you say, If we only have to look back em toe or n plus one terms and each of those terms is in the range of one to em, then there would only be M to the M possible terms.

Supposing that there is a biggest number at we look a chunk of length M that determines everything from that point on.

But then you say there are only em to the M different chunks, so one of them will have to repeat, so the sequence will be periodic.

So from a certain point on, the sequence will repeat.

But that contact I want to see the proof.

So here's the sequence, and this part is the period.

From then on, it just keeps repeating over and over again and let me prove that can't happen.

Say it begins with ex dot, dot, dot and it ends with a Z in the next period.

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

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