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Math Help - I need help finding the next term

  1. #1
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    I need help finding the next term

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

    HELP!!!
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  2. #2
    MHF Contributor
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    Talking

    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?
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  3. #3
    Super Member

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    Lexington, MA (USA)
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    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<br />
\text{Term} & \text{Description} \\ \hline \hline<br />
1 & \text{one 1} \\<br />
11 & \text{two 1s} \\<br />
21 & \text{one 2, one 1} \\<br />
1211 & \text{one 1, one 2, two 1s} \\<br />
111221 & \text{three 1s, two 2s, one 1} \\<br />
312211 & \text{one 3, one 1, two 2s, two 1s} \\<br />
13112221 & \text{one 1, one 3 two 1s, three 2's, one 1} \\<br />
{\color{blue}1113213211} & \\ \hline\end{array}



    Edit: Ha! . . . Too slow again!
    .
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  4. #4
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    wait so there is no actuall formula

    Okay so if that is correct then there is no actual formula
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  5. #5
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    --------------------------------------------------------------------------------

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