I need help finding the next term

**kandela573** · December 11th 2009, 07:56 AM

I need help figuring out the next term:
1, 11, 21, 1211, 111221, 312211, 13112221, _?

HELP!!!

**stapel** · December 11th 2009, 08:08 AM

This isn't actually math, so I don't feel to bad about giving a big hint.

1

Describing the above, we have "one 1".

11

Describing the above, we have "two 1's".

21

Describing the above, we have "one 2 and one 1".

1211

Describing the above, we have "one 1, one 2, and two 1's".

111221

Can you see where to go from there?

**Soroban** · December 11th 2009, 08:08 AM

Hello, kandela573!

This is a classic (very old) problem ... with a very sneaky answer.

Find the next term: . $1,\;11,\;21,\; 1211,\; 111221,\; 312211,\; 13112221,\;\hdots$

The sequence begins with "1".

Each successive term is a description of the previous number.

. . $\begin{array}{|c|c|} \hline \text{Term} & \text{Description} \\ \hline \hline 1 & \text{one 1} \\ 11 & \text{two 1s} \\ 21 & \text{one 2, one 1} \\ 1211 & \text{one 1, one 2, two 1s} \\ 111221 & \text{three 1s, two 2s, one 1} \\ 312211 & \text{one 3, one 1, two 2s, two 1s} \\ 13112221 & \text{one 1, one 3 two 1s, three 2's, one 1} \\ {\color{blue}1113213211} & \\ \hline\end{array}$

Edit: Ha! . . . Too slow again!
.

**kandela573** · December 11th 2009, 08:15 AM

Okay so if that is correct then there is no actual formula

**kandela573** · December 11th 2009, 08:58 AM

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Okay so if that is correct then there is no actual formula right?

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I need help finding the next term

wait so there is no actuall formula

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