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Got this series from a friend in this patricular form:

  1 2 1 1
  1 2 3 1
2 1 1 2 1 3
2 2 3 1 1 3
?????????????

I don't really know if the form has anything to do with the series and don't know if it is a mathematical series... any clues on what is next and most importantly why?

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1  
It would help if you were to give context for where this quetsion comes from. –  Jonah Sinick Apr 1 '13 at 4:42
    
no context around it... it's just that on an empty notebook page... there is a change the follow up is: 222321 421311 11123113 , but not sure if this is right. He told me that these 4 lines where enough to figure it out. –  George F-bot Apr 1 '13 at 4:44

2 Answers 2

up vote 1 down vote accepted

It's similar to the look-and-say but you count the TOTAL number occurrences of the first integer in the above line then proceed to the next integer that appears.

1

11

21

1211

1231

211213

223113

222321

321311

231231

222321

421311

14123113 . . .

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it's correct!! thanks!! but why 1231 isn't 3112 like the rest of the lines? first comes the 1 in the above line... –  George F-bot Apr 1 '13 at 6:55
    
Hmmm I missed that one. If your friend said it's correct then he made an error as well. –  user47805 Apr 1 '13 at 15:36

This looks similar to $1,11,21,1211,111221$ which is OEIS A005150 the look-and-say sequence but I can't make the correspondence.

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