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This is a slight variation on an old puzzle that's likely already here, but be sure to check it before you mark it as duplicate.

What are the next three terms in this sequence, and why? 

 1  
 11  
 21  
 1211  
 1231  
 131221  
 132231  
 232221  
 ...

Edit: This is not the Look-and-say sequence as the duplicate links are. It is a variation on the idea of them, but it is not a duplicate in my opinion.

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    $\begingroup$ Please check for duplicates before posting. There are already 3 examples of this sequence on this site (one, two, three). Although they may not be exactly the same, they are close enough to be called duplicates. $\endgroup$ – Len May 6 '15 at 3:18
  • $\begingroup$ @Len Actually this isn't a duplicate! Check the accepted answer, and the latest edit to the question. I've voted to reopen. $\endgroup$ – Rand al'Thor May 6 '15 at 22:38
  • $\begingroup$ @randal'thor - As I stated above, I think it is close enough to be called a duplicate. Feel free to vote however you want. $\endgroup$ – Len May 6 '15 at 22:48
  • $\begingroup$ @randal'thor Thank you. I tried to make it different enough and explain that there are some similarities without being the exact same puzzle. $\endgroup$ – Spencerkatty May 7 '15 at 0:29
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To answer the question more precisely, these are the next three terms:

134211
14131231
14231241

This is a variant of the Look-and-say sequence. This particular variant is already in OEIS! It is formed by summarizing the terms of the previous number, but all at once in descending order, which is different from the look and say sequence.

For example, the sequence goes from 1211 to 1231 because:
The previous term contained one two. (12)
The previous term contained three ones. (31)
-> 1231.

Another example, the sequence goes from 132231 to 232221 because:
The previous term contained two threes. (23)
The previous term contained two twos. (22)
The previous term contained two ones. (21)
-> 232221.

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This is like that look-say sequence thing. Each line describes the numbers of the line before.

First line has one 1, so the second line is 11. The second line has 2 1's, so the third line is 21. The third line has one two and one one, so the fourth line is 1211 etc.

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  • $\begingroup$ Close, but you don't give the next terms, and it's not quite the look-and-say sequence. $\endgroup$ – Spencerkatty May 7 '15 at 0:32

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