Can you find the next number in this sequence

你能找到這個(gè)數(shù)列下一個(gè)數(shù)字嘛

來(lái)源視頻

These are the first five elements of a number sequence.

Can you figure out what comes next?

Pause here if you want ?to figure it out for yourself.

Answer in:?3?

Answer in: 2

Answer in: 1

這些是一個(gè)數(shù)列最開(kāi)始的五個(gè)數(shù)字。

你能想出下一個(gè)數(shù)字是什么嗎？

如果你想要自己先想清楚的話 就在這里暫停一下。

答案倒數(shù) 3

答案倒數(shù)?2?

答案倒數(shù) 1

There is a pattern here,

but it may not be the kind of pattern you think it is.

Look at the sequence again and try reading it aloud.

Now, look at the next number in the sequence.

3 ,1 ,2?,2?,1?,1?.

Pause again if you'd like to think about it some more.

Answer in: 3

Answer in: 2

Answer in: 1

這個(gè)數(shù)列有一個(gè)規(guī)律，

然而這個(gè)規(guī)律可能不是你所想的那樣。

重新再看一下這個(gè)數(shù)列。

并嘗試讀出聲來(lái)。

現(xiàn)在，讓我們來(lái)看這一數(shù)列的下一個(gè)數(shù)字。

3，1，2，2，1，1

如果你需要多思考一下的話 可以再暫停一下。

答案倒數(shù) 3

答案倒數(shù) 2

答案倒數(shù) 1

This is what's known as a look and say sequence.

Unlike many number sequences,

this relies not on some mathematical property of the numbers themselves,

but on their notation.

Start with the left-most digit of the initial number.

Now, read out how many times ?it repeats in succession

followed by the name of the digit itself.

Then move on to the next distinct digit and repeat until you reach the end.

這就是所謂的外觀數(shù)列，

和其它的數(shù)字?jǐn)?shù)列不同，

這個(gè)數(shù)列的規(guī)律并不依靠于 數(shù)字自身的的數(shù)學(xué)屬性，

而是數(shù)字的表示法。

從初始數(shù)字的最左數(shù)位開(kāi)始讀起。

現(xiàn)在讀出它連續(xù)重復(fù)的次數(shù)，

然后再讀出這一數(shù)字。

下一個(gè)數(shù)位的讀法也是依此類(lèi)推。

直到讀完最后一位。

So the number ?is read as "one one"

written down the same way ?we write eleven.

Of course, as part of this sequence, it's not actually the number eleven,

but 2?ones,

which we then write as 2 1?.

That number is then read out as 1 2 1 1?,

which written out we'd read as one one, one two, two ones, and so on.

所以數(shù)字讀作“一個(gè)一”，

和我們寫(xiě)數(shù)字十一的方法一樣。

自然，作為這個(gè)數(shù)列的一部分，

11并不是真正的數(shù)字十一，

而是“兩個(gè)一”，

因此我們又寫(xiě)作21。

而這個(gè)數(shù)字讀出來(lái)是 1 2 1 1?，

而1211寫(xiě)出來(lái)又可讀作 一個(gè)一、一個(gè)二、二個(gè)一，

以此類(lèi)推。

These kinds of sequences were first analyzed by mathematician John Conway,

who noted they have ?some interesting properties.

For instance, starting with the number?22, yields an infinite loop of two twos.

But when seeded with any other number,

the sequence grows in some very specific ways.

Notice that although the number of digits keeps increasing,

the increase doesn't seem to be either linear or random.

這個(gè)數(shù)列最初是由數(shù)學(xué)家 John Conway 所發(fā)現(xiàn)，

他注意到了這一數(shù)列一些很有趣的屬性。

比如從數(shù)字22開(kāi)始， 這一數(shù)列會(huì)生成的“二個(gè)二”的無(wú)窮循環(huán)。

但如果我們從其他數(shù)字開(kāi)始的話，

這個(gè)數(shù)列就會(huì)以一些特殊的方式展開(kāi)。

請(qǐng)注意，雖然這些數(shù)字的位數(shù)數(shù)量在不斷增長(zhǎng)，

這些增長(zhǎng)似乎并不是線性的或隨機(jī)的。

In fact, if you extend the sequence infinitely, a pattern emerges.

The ratio between the amount of digits in two consecutive terms

gradually converges to a single number known as Conway's Constant.

This is equal to a little over 1.3,

meaning that the amount of digits increases by about 30%

with every step in the sequence.

事實(shí)上，如果你把這個(gè)數(shù)列無(wú)限擴(kuò)大，

規(guī)律就會(huì)浮現(xiàn)出來(lái)。

相鄰兩個(gè)數(shù)字的數(shù)位數(shù)量之間的比例，

會(huì)逐漸趨近 一個(gè)被稱(chēng)為“Conway常數(shù)”的數(shù)字。

這一數(shù)字會(huì)比1.3稍大一點(diǎn)，

也就是說(shuō)，數(shù)列中每生成下一項(xiàng)數(shù)字，

數(shù)位的數(shù)量大約增長(zhǎng)30%。

with every step in the sequence.

What about the numbers themselves?

That gets even more interesting.

Except for the repeating sequence of 22,

every possible sequence eventually breaks down into distinct strings of digits.

No matter what order these strings show up in,

each appears unbroken in its entirety every time it occurs.

那么，那些數(shù)字本身如何呢？

這就更加有趣了。

除了22這一無(wú)限循環(huán)的數(shù)列，

每一個(gè)可能的數(shù)列最終會(huì) 被分解成不同的數(shù)位字符串。

不論這些字符串以怎樣的順序出現(xiàn)，

它們都會(huì)不斷延續(xù)下去。

Conway identified 92?of these elements,

all composed only of digits 1, 2, and 3 ,

as well as two additional elements

whose variations can end with any digit of 4?or greater.

No matter what number the sequence is seeded with,

eventually, it'll just consist of these combinations,

with digits 4?or higher only appearing at the end of the two extra elements,

if at all.

Conway 分析了92個(gè)字符串，

所有的字符串只包含數(shù)字1、2和 3

以及其他兩個(gè)變化的字符串，

它們以大于或等于4的數(shù)字結(jié)尾。

無(wú)論從哪一個(gè)數(shù)字開(kāi)始這一數(shù)列，

數(shù)列最終都會(huì)包含以上這些字符串的組合。

大于或等于4的數(shù)字 只出現(xiàn)在兩個(gè)變化字符串的末尾，

如果出現(xiàn)的話。

Beyond being a neat puzzle,

the look and say sequence has some practical applications.

For example, run-length encoding,

a data compression that was once used for television signals and digital graphics,

is based on a similar concept.

The amount of times a data value repeats within the code

is recorded as a data value itself.

Sequences like this are a good example of how numbers and other symbols

can convey meaning on multiple levels.

除了作為一個(gè)工整有序的數(shù)字謎題之外，

外觀數(shù)列也被應(yīng)用到實(shí)際中。

以游程編碼為例，

它從前被運(yùn)用到電視信號(hào)和 數(shù)碼圖像的數(shù)據(jù)壓縮上。

游程編碼也是建立在一個(gè)相似的概念上，

在編碼中， 數(shù)據(jù)出現(xiàn)的次數(shù)被記作數(shù)據(jù)值。

這樣的數(shù)列就是一個(gè)很好的例子，

表現(xiàn)數(shù)字和其他符號(hào)是 怎樣在多層次方面?zhèn)鬟_(dá)含義的。