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What is the next three numbers for this pattern? 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, 1321131112311

I can only get the first two. I can't figure out the rest.

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Hassan H. | Math Tutor (All Levels)Math Tutor (All Levels)
5.0 5.0 (176 lesson ratings) (176)
1
Casadi,
 
You have stumbled upon a series that I used to give my students as a fun challenge!  If you really are stuck, I'll give the answer below, but don't look if you still want to give it a shot!
 
The first number is 1, so say "one."  Now, to form the next number, tell me what I have in the previous one---"one one"---so write 11.  Then, the next consists of "two ones", so write 21.  The next consists of "one two, one one", so write 1211, etc.  Keep reading the previous number in terms of blocks of any given digit, and you'll have your sequence.
 
Very smart-alecky type of recursive sequence, and it always elicits a groan from the audience once they hear the answer.
 
Regards,
Hassan H.
Rusty P. | Math can be Fun, or at least toleratedMath can be Fun, or at least tolerated
0

Groan.  :)