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Subj:     MATH PROB. - Conway Sequence (S468)
          From: William Wu of U. C. Berkeley on 1/13/2006
          At: http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml
 Source: http://www.ocf.berkeley.edu/~wwu/riddles/medium.shtml#conwaySequence

What row of numbers comes next?

 1
 11
 21
 1211
 111221
 312211
 13112221

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Solution from Abe

Each line of numbers describes the previous line.

 1
 11        = one one
 21        = two ones
 1211      = one two, and one one
 111221    = one one, one two, and two ones
 312211    = three ones, two twos, and one one
 13112221  = one three, one one, two twos, and two ones

Therefore Abe's new line is

 1113213211 = one one, one three, two ones, three twos, and one one

Thank you Abe for showing me the way.