I need help figuring out the next term:
1, 11, 21, 1211, 111221, 312211, 13112221, _?
HELP!!!
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?
Hello, kandela573!
This is a classic (very old) problem ... with a very sneaky answer.
Find the next term: .$\displaystyle 1,\;11,\;21,\; 1211,\; 111221,\; 312211,\; 13112221,\;\hdots$
The sequence begins with "1".
Each successive term is a description of the previous number.
. . $\displaystyle \begin{array}{|c|c|} \hline
\text{Term} & \text{Description} \\ \hline \hline
1 & \text{one 1} \\
11 & \text{two 1s} \\
21 & \text{one 2, one 1} \\
1211 & \text{one 1, one 2, two 1s} \\
111221 & \text{three 1s, two 2s, one 1} \\
312211 & \text{one 3, one 1, two 2s, two 1s} \\
13112221 & \text{one 1, one 3 two 1s, three 2's, one 1} \\
{\color{blue}1113213211} & \\ \hline\end{array}$
Edit: Ha! . . . Too slow again!
.