121, 111211, 311221 Puzzle (Look and Say Sequence)

Date: 10/23/2001 at 18:53:18
From: Joey
Subject: What's the next number?

121, 111211, 311221  - what's the next number?

Date: 10/23/2001 at 22:28:06
From: Doctor Paul
Subject: Re: What's the next number?

The first number is 121. If you were to describe this number to 
someone who was writing it down digit by digit, you would say:

Write down a single one - that is, one one. Then write down a single 
two - that is, one two. Finally, write down a single one - that is, 
one one.

Put them together: one one one two one one

Notice that this gives the next number:  111211

To describe this number in words digit by digit gives:

   three ones, one two, two ones = 311221

A similar pattern shows that the next numbers in the sequence are:

   13212211, 111312112221, 31131112213211

- Doctor Paul, The Math Forum
  http://mathforum.org/dr.math/