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Thread: Can you figure out this pattern?

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  1. Mar 2nd, 2009, 04:02 PM #1
    timeshifter
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    Can you figure out this pattern?

    Code:
    1
11
21
1211
111221
312211
...
    After much fiddling, I finally got a program written that accurately figures it out... I personally love it. It's a very simple pattern to grasp from a conceptual standpoint, but the actual math for it is pretty maddening.. hence why I didn't even use any math in the app...
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  2. Mar 2nd, 2009, 05:19 PM #2
    techgnome
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    Re: Can you figure out this pattern?

    hmmm... I believe that's the mathematical representation of the Pinocchio Paradox, is not not?

    -tg
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  3. Mar 2nd, 2009, 10:11 PM #3
    EntityX
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    Re: Can you figure out this pattern?

    Quote Originally Posted by techgnome
    hmmm... I believe that's the mathematical representation of the Pinocchio Paradox, is not not?

    -tg
    Does the Pinocchio Paradox have to do with Pinocchio's nose?
    Make as many mistakes as you can as quickly as you can. We want to make sure that we make a great enough number of mistakes in a given amount of time so that we can be successful.

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  4. Mar 2nd, 2009, 05:47 PM #4
    timeshifter
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    Re: Can you figure out this pattern?

    There is a mathematical formula for this pattern... but it's extremely ugly... and no, it has no relation to the Pinocchio Paradox that I'm aware of
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  6. Mar 2nd, 2009, 08:37 PM #5
    System_Error
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    Re: Can you figure out this pattern?

    Quote Originally Posted by timeshifter
    There is a mathematical formula for this pattern... but it's extremely ugly... and no, it has no relation to the Pinocchio Paradox that I'm aware of
    There's a mathematical formula for this?
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  7. Mar 2nd, 2009, 08:36 PM #6
    System_Error
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    Re: Can you figure out this pattern?

    Quote Originally Posted by timeshifter
    Code:
    1
11
21
1211
111221
312211
...
    After much fiddling, I finally got a program written that accurately figures it out... I personally love it. It's a very simple pattern to grasp from a conceptual standpoint, but the actual math for it is pretty maddening.. hence why I didn't even use any math in the app...
    Start with 1, then each proceeding sequence describes the previous.

    11 -> reads there is one 1
    21 -> reads there is two 1's
    1211 -> reads there is one 2 and one 1
    etc

    I think.
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  8. Mar 2nd, 2009, 10:47 PM #7
    timeshifter
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    Re: Can you figure out this pattern?

    Quote Originally Posted by System_Error
    Start with 1, then each proceeding sequence describes the previous.

    11 -> reads there is one 1
    21 -> reads there is two 1's
    1211 -> reads there is one 2 and one 1
    etc

    I think.
    Correct. The program I wrote treats the number as a string, not a number... works pretty well, but don't run it past 30 numbers or so... it gets exponentially bigger.

    Quote Originally Posted by System_Error
    There's a mathematical formula for this?
    Quote Originally Posted by http://dheera.net/sci/sequence_sol.php
    ...(D is a recursive function and t is the term number.)
    ...
    % here is a certain non-integer remainder function. 2.1%0.1 would be 0, 2.1%0.2 would be 0.1, 2.1%0.3 would be 0 since 0.3 fits evenly into 2.1, etc.) If you really want conventional operators, you could define % with limits and modular arithmetic...

    D(t+1) = (sigma(K=1,LOG(D(t)*10)-LOG(D(t)*10)%1,((D(t)-D(t)%10^(LOG(D(t))-
    LOG(D(t))%1)+sigma(S=1,LOG(D(t))-LOG(D(t))%1,(((sigma(R=1,LOG(D(t)*10)
    -LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*
    10%10^R)%10^(R+1)))/10)-(sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*
    10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)
    %10^(S-1))%10^S+1)%(((sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)
    *10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)-(
    sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%10
    ^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)%10^(S-1))%10^S+.5)*2*(D(t)
    -D(t)%10^(S-1))%10^S))-(D(t)-D(t)%10^(LOG(D(t))-LOG(D(t))%1)+sigma(S=1,
    LOG(D(t))-LOG(D(t))%1,(((sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)
    *10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)
    -(sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%
    10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)%10^(S-1))%10^S+1)%(((
    sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%
    10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)-(sigma(R=1,LOG(D(t)*
    10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*
    10-D(t)*10%10^R)%10^(R+1)))/10)%10^(S-1))%10^S+.5)*2*(D(t)-D(t)%10^(S
    -1))%10^S))%10^(K-1))%10^K/10^(K-1)*100^(2*sigma(N=1,K,(((D(t)-D(t)%
    10^(LOG(D(t))-LOG(D(t))%1)+sigma(S=1,LOG(D(t))-LOG(D(t))%1,(((sigma(R=1,
    LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%10^(R+2)/10-
    (D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)-(sigma(R=1,LOG(D(t)*10)-LOG(D(t)*
    10)%1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%
    10^(R+1)))/10)%10^(S-1))%10^S+1)%(((sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%
    1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%
    10^(R+1)))/10)-(sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)
    *10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)%10^(S-1))
    %10^S+.5)*2*(D(t)-D(t)%10^(S-1))%10^S))-(D(t)-D(t)%10^(LOG(D(t))-LOG(D(t))
    %1)+sigma(S=1,LOG(D(t))-LOG(D(t))%1,(((sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)
    %1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^
    (R+1)))/10)-(sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)*10%
    10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)%10^(S-1))%10^
    S+1)%(((sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)*10%10^
    (R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)-(sigma(R=1,
    LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%10^(R+2)/
    10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)%10^(S-1))%10^S+.5)*2*(D(t)-D(t)%
    10^(S-1))%10^S))%10^(N-1))%10^N+1)%(((D(t)-D(t)%10^(LOG(D(t))-LOG(D(t))%
    1)+sigma(S=1,LOG(D(t))-LOG(D(t))%1,(((sigma(R=1,LOG(D(t)*10)-LOG(D(t)*
    10)%1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^
    R)%10^(R+1)))/10)-(sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-
    D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)%10^
    (S-1))%10^S+1)%(((sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-
    D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)-
    (sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%
    10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)%10^(S-1))%10^S+.5)*2*
    (D(t)-D(t)%10^(S-1))%10^S))-(D(t)-D(t)%10^(LOG(D(t))-LOG(D(t))%1)+
    sigma(S=1,LOG(D(t))-LOG(D(t))%1,(((sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10
    )%1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^
    R)%10^(R+1)))/10)-(sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*
    10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/
    10)%10^(S-1))%10^S+1)%(((sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,
    ABS((D(t)*10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%
    10^(R+1)))/10)-(sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*
    10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))
    /10)%10^(S-1))%10^S+.5)*2*(D(t)-D(t)%10^(S-1))%10^S))%10^(N-1))%10^
    N+.5))))/100)+(sigma(K=1,LOG(D(t)*10)-LOG(D(t)*10)%1,100^(1+sigma(N=
    1,K-1,2*((((sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)*
    10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)-(
    sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%
    10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)%10^(N-1))%10^N/10^(N-
    1)+1)%(((sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)*10%
    10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)-(sigma(R=
    1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%10^(R+
    2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)%10^(N-1))%10^N/10^(N-1)+
    .5)))))/10)
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  9. Mar 3rd, 2009, 08:04 AM #8
    BillGeek
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    Re: Can you figure out this pattern?

    That looks... slightly disturbing.

    Anyone able to narrow that down?
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  11. Mar 4th, 2009, 01:54 AM #9
    mendhak
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    Re: Can you figure out this pattern?

    Quote Originally Posted by BillGeek
    That looks... slightly disturbing.

    Anyone able to narrow that down?
    Here you go:

    D(t+1) = (sigma(K=1,LOG(D(t)*10)-LOG(D
    (t)*10)%1,((D(t)-D(t)%10^(LOG(D(t))-
    LOG(D(t))%1)+sigma(S=1,LOG(D(t))-LOG(D
    (t))%1,(((sigma(R=1,LOG(D(t)*10)
    -LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)*10%
    10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*
    10%10^R)%10^(R+1)))/10)-(sigma(R=1,LOG
    (D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*
    10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)
    *10-D(t)*10%10^R)%10^(R+1)))/10)
    %10^(S-1))%10^S+1)%(((sigma(R=1,LOG(D
    (t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)
    *10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)
    *10-D(t)*10%10^R)%10^(R+1)))/10)-(
    sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,
    ABS((D(t)*10-D(t)*10%10^(R+1))%10
    ^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^(R+1
    )))/10)%10^(S-1))%10^S+.5)*2*(D(t)
    -D(t)%10^(S-1))%10^S))-(D(t)-D(t)%10^(
    LOG(D(t))-LOG(D(t))%1)+sigma(S=1,
    LOG(D(t))-LOG(D(t))%1,(((sigma(R=1,LOG(D
    (t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)
    *10-D(t)*10%10^(R+1))%10^(R+2)/10-(D
    (t)*10-D(t)*10%10^R)%10^(R+1)))/10)
    -(sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1
    -1,ABS((D(t)*10-D(t)*10%10^(R+1))%
    10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10
    ^(R+1)))/10)%10^(S-1))%10^S+1)%(((
    sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)
    %1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%
    10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10
    ^(R+1)))/10)-(sigma(R=1,LOG(D(t)*
    10)-LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)
    *10%10^(R+1))%10^(R+2)/10-(D(t)*
    10-D(t)*10%10^R)%10^(R+1)))/10)%10^(S-1
    ))%10^S+.5)*2*(D(t)-D(t)%10^(S
    -1))%10^S))%10^(K-1))%10^K/10^(K-1)*100
    ^(2*sigma(N=1,K,(((D(t)-D(t)%
    10^(LOG(D(t))-LOG(D(t))%1)+sigma(S=1,LOG
    (D(t))-LOG(D(t))%1,(((sigma(R=1,
    LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*
    10-D(t)*10%10^(R+1))%10^(R+2)/10-
    (D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)-(
    sigma(R=1,LOG(D(t)*10)-LOG(D(t)*
    10)%1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%
    10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%
    10^(R+1)))/10)%10^(S-1))%10^S+1)%(((
    sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%
    1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%10
    ^(R+2)/10-(D(t)*10-D(t)*10%10^R)%
    10^(R+1)))/10)-(sigma(R=1,LOG(D(t)*10)
    -LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)
    *10%10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)
    *10%10^R)%10^(R+1)))/10)%10^(S-1))
    %10^S+.5)*2*(D(t)-D(t)%10^(S-1))%10^S))
    -(D(t)-D(t)%10^(LOG(D(t))-LOG(D(t))
    %1)+sigma(S=1,LOG(D(t))-LOG(D(t))%1,
    (((sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)
    %1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%10
    ^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^
    (R+1)))/10)-(sigma(R=1,LOG(D(t)*10)-LOG
    (D(t)*10)%1-1,ABS((D(t)*10-D(t)*10%
    10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%
    10^R)%10^(R+1)))/10)%10^(S-1))%10^
    S+1)%(((sigma(R=1,LOG(D(t)*10)-LOG(D(t)*
    10)%1-1,ABS((D(t)*10-D(t)*10%10^
    (R+1))%10^(R+2)/10-(D(t)*10-D(t)*10%10^R)
    %10^(R+1)))/10)-(sigma(R=1,
    LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS((D(t)*
    10-D(t)*10%10^(R+1))%10^(R+2)/
    10-(D(t)*10-D(t)*10%10^R)%10^(R+1)))/10)
    %10^(S-1))%10^S+.5)*2*(D(t)-D(t)%
    10^(S-1))%10^S))%10^(N-1))%10^N+1)%(((D
    (t)-D(t)%10^(LOG(D(t))-LOG(D(t))%
    1)+sigma(S=1,LOG(D(t))-LOG(D(t))%1,(((
    sigma(R=1,LOG(D(t)*10)-LOG(D(t)*
    10)%1-1,ABS((D(t)*10-D(t)*10%10^(R+1))
    %10^(R+2)/10-(D(t)*10-D(t)*10%10^
    R)%10^(R+1)))/10)-(sigma(R=1,LOG(D(t)*10
    )-LOG(D(t)*10)%1-1,ABS((D(t)*10-
    D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*10-D
    (t)*10%10^R)%10^(R+1)))/10)%10^
    (S-1))%10^S+1)%(((sigma(R=1,LOG(D(t)*10)
    -LOG(D(t)*10)%1-1,ABS((D(t)*10-
    D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*10-D
    (t)*10%10^R)%10^(R+1)))/10)-
    (sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)%1-1
    ,ABS((D(t)*10-D(t)*10%10^(R+1))%
    10^(R+2)/10-(D(t)*10-D(t)*10%10^R)%10^
    (R+1)))/10)%10^(S-1))%10^S+.5)*2*
    (D(t)-D(t)%10^(S-1))%10^S))-(D(t)-D(t)%
    10^(LOG(D(t))-LOG(D(t))%1)+
    sigma(S=1,LOG(D(t))-LOG(D(t))%1,(((sigma
    (R=1,LOG(D(t)*10)-LOG(D(t)*10
    )%1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%10^
    (R+2)/10-(D(t)*10-D(t)*10%10^
    R)%10^(R+1)))/10)-(sigma(R=1,LOG(D(t)*10)
    -LOG(D(t)*10)%1-1,ABS((D(t)*
    10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)*
    10-D(t)*10%10^R)%10^(R+1)))/
    10)%10^(S-1))%10^S+1)%(((sigma(R=1,LOG
    (D(t)*10)-LOG(D(t)*10)%1-1,
    ABS((D(t)*10-D(t)*10%10^(R+1))%10^(R+2)
    /10-(D(t)*10-D(t)*10%10^R)%
    10^(R+1)))/10)-(sigma(R=1,LOG(D(t)*10)
    -LOG(D(t)*10)%1-1,ABS((D(t)*
    10-D(t)*10%10^(R+1))%10^(R+2)/10-(D(t)
    *10-D(t)*10%10^R)%10^(R+1)))
    /10)%10^(S-1))%10^S+.5)*2*(D(t)-
    D(t)%10^(S-1))%10^S))%10^(N-1))%10^
    N+.5))))/100)+(sigma(K=1,LOG(D(t)
    *10)-LOG(D(t)*10)%1,100^(1+sigma(N=
    1,K-1,2*((((sigma(R=1,LOG(D(t)*10)
    -LOG(D(t)*10)%1-1,ABS((D(t)*10-D(t)*
    10%10^(R+1))%10^(R+2)/10-(D(t)*10-
    D(t)*10%10^R)%10^(R+1)))/10)-(
    sigma(R=1,LOG(D(t)*10)-LOG(D(t)*10)
    %1-1,ABS((D(t)*10-D(t)*10%10^(R+1))%
    10^(R+2)/10-(D(t)*10-D(t)*10%10^R)
    %10^(R+1)))/10)%10^(N-1))%10^N/10^(N-
    1)+1)%(((sigma(R=1,LOG(D(t)*10)-LOG
    (D(t)*10)%1-1,ABS((D(t)*10-D(t)*10%
    10^(R+1))%10^(R+2)/10-(D(t)*10-D(t)
    *10%10^R)%10^(R+1)))/10)-(sigma(R=
    1,LOG(D(t)*10)-LOG(D(t)*10)%1-1,ABS
    ((D(t)*10-D(t)*10%10^(R+1))%10^(R+
    2)/10-(D(t)*10-D(t)*10%10^R)%10^
    (R+1)))/10)%10^(N-1))%10^N/10^(N-1)+
    .5)))))/10)
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  12. Mar 3rd, 2009, 10:55 AM #10
    MaximilianMayrhofer
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    Re: Can you figure out this pattern?

    Quote Originally Posted by BillGeek
    That looks... slightly disturbing.

    Anyone able to narrow that down?
    Code:
    while (true) { Console.WriteLine("All your cpu is belong to my loop!"); }
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  13. Mar 4th, 2009, 07:54 AM #11
    wossname
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    Re: Can you figure out this pattern?

    ts: Is there actually a use for this of are you just sto-... bored?

    Fun though...
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    Last edited by wossname; Mar 4th, 2009 at 08:18 AM.
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  14. Mar 4th, 2009, 11:02 AM #12
    timeshifter
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    Re: Can you figure out this pattern?

    Wow... you're mad.
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