Subtitles section Play video Print subtitles 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 misleading. 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.

A2 sequence hint calmer enclosed misleading draw What Number Comes Next? - Numberphile 5 0 林宜悉 posted on 2020/03/27 More Share Save Report Video vocabulary