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• What's the next term?

• In the following sequence it goes 148 48 88 4 88 What's the next term?

• Which actually is very easy and why that's not so obvious?

• Well, well, it's a little strange for 8 48 88 for a date, and obviously the next one is going to be 888 and then 4888 The right way to look at this.

• It's to stare at these numbers.

• Look at this number.

• What do you see?

• Well, you see eight.

• But more important, you see two holes.

• When you look at 48 you see three holes.

• 88 has four holes in it.

• Four has one home if you draw affords that way, and one has no holes in it.

• So the definition of this sequence is it's the smallest positive number that has n holds in it.

• People always get really funny about sequences and numbers that are sort of based 10 specific.

• This is This is how you draw your numbers specifically.

• If you draw your four non enclosed, it would be it would change the sequence.

• In that case, if you for is not enclosed.

• Then you would make it 168 68 88 688 and so on.

• And if you do your twos in a very fancy way with a hole in them, then the six could be replaced by two.

• This is topology him.

• What we're doing is petitioning the piece of paper in tow parts without using numbers.

• So if you write down a four, you've partitioned the plane into two pods, this part on the outside.

• So it's topology.

• This one is another base 10 sequence, so but it's lovely.

• 61 2182 43 3 And the question is, what comes next?

• Don't get distracted into looking for something that's too complicated.

• Watch carefully.

• There's nothing up my sleeve.

• I'm just going to move the calmer, and I'm gonna move that calmer than that that come up and there's an invisible zero.

• And so the next one.

• Get it?

• 6 12 18 24 30 say 36.

• So that one after that would be 42.

• They're multiples of six.

• Nothing could be simpler, but if you were misled into looking for something complicated you wouldn't get that is sneaky.

• That one.

• Yeah, yeah, yeah, yeah, I like it.

• It's deceptive.

• Slight of hand one.

• We get zero to forget.

• Sierra three, we get zero for we get zero.

• This doesn't look too promising.

• All right?

• Is it ever going to get more than Sarah yet?

• Five.

• We get four six, we get 97 you get five eight to get 19 we get one 10.

• I'll do a couple more to make.

• 10.

• We get 0 11 You'll never guess what we get for 11 55.

• What's the rule?

• Let me show you the answer.

• I put the squares on top of the numbers and you look through the window.

• You have to think like a room.

• The ivy.

• Four.

• I hex.

• Nine.

• The five 81 There's a single 1910 is nothing.

• 11 is 55 so on.

• That would have taken me a year s.

• So, of course, it might not be a legal Roman number.

• You might have the ones and the V's and the M's in the wrong order.

• In which case, the way the sequence would be defined as you say that zero for that too.

• closely related sequences in the sense that they both have names.

• They both have slightly misleading names.

• Titles on the 1st 1 the even numbers.

• Well, you know what the even numbers are.

• 2468 But I would like you to figure out what the even numbers are, too.

• I have to be very careful for 677 is not even 89 10 11 12 12 30 It's the next even number.

• And then 32 34 36 40 42 44 50 52 54 56.

• You getting the idea?

• 60.

• Let me continue 60 to 64.

• 66 2000.

• There's any even numbers.

• 2000.

• That was a jump.

• Why are those three even numbers?

• What do you notice about these numbers?

• For one thing, they're all even.

• The second thing is that if you if you write out the number in English, there are no ease in them.

• One is missing because one has an E in it.

• Three has an e in it ate, hasn't he in it?

• In fact, there's a theory.

• Um, it's an old theorem of mine.

• Every hard number contains an e.

• And you can easily prove that by looking at all the odd numbers and check why they called even numbers e is banned and the other questions Let me show you another one with a name.

• These are the e mopes, and again the name is a hint, and in this case, it's actually a legitimate hint theme.

• Herbs, as you might guess.

• Well, let me show you what they look like, first of all, and then you can guess.

• 13.

• 17 then, um, her.

• It's not 19.

• You might have thought I was gonna write 19 but it's actually 31 37 71 that's probably enough of a hint.

• Well, obviously they're primes.

• And if you look at the name, you see its prime backwards.

• So these are the primes, which, when you read them backwards, are still primes but different crimes.

• So we don't put out 11 because it's palindrome.

• Make thes of primes, which, when you read it backwards, gives you a different crime.

• I know what you're all thinking.

• Everyone.

• What is the largest known e Murph?

• A sw.

• Far as I can tell, it's this or its decimal expansion.

• Is this nephew like these fun little puzzles.

• I've actually got one left over, one that got cut from this video, but still pretty good fun.

• I've put it over on the number filed to channel.

• There's links on the screen and in the description, and we'll have new Sloan back really soon.

• Talking about Maur amazing sequences from his online encyclopedia.

• Stay tuned for that.

What's the next term?

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# What Number Comes Next? - Numberphile

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林宜悉 posted on 2020/03/27
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