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  • 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

  • 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

  • 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.

  • So the number 1 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

These are the first five elements of a number sequence.

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【TED-Ed】你可以在這個序列中找到下一個數字嗎? - 亞歷克斯·甘德勒 (Can you find the next number in this sequence? - Alex Gendler) ()

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    X69599596 發佈於 2017 年 07 月 29 日
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