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Friday, November 28, 2008

Call for Papers

0) We'll define this binary sequence in stages, punctuated by periods for clarity. (The periods are cosmetic; they are not part of the sequence.)

1) The first stage: 0.

2) The next stage: 1. So far: 0.1.

3) The next stage: a copy of all previous stages except the last: 0. So far: 0.1.0.

4) The next stage: same as for (3): 01. So far: 0.1.0.01.

5) Etc.: 0.1.0.01.010.01001.01001010.0100101001001. ...

6) Stripped of ".": 0100101001001010010100100101001001 ...

7) What, if anything, can you say about this sequence? This is not a "problem," I'd really like to know.

8) What, if any, reward in Heaven do you expect for your conscientious application to (7)?

4 comments:

  1. wow this is beyond my knowledge of rocket science..

    huhu im confused..

    ReplyDelete
  2. OK, well, here are a couple of observations to get you started:

    a) If you encode
    010 --> 0
    01 --> 1
    then the same sequence is recovered. Which means what??

    b) It's also not hard to see that the sequence consists only of '01' and '001' so encode
    01 --> 0
    001 --> 1
    then you get: 0101101011011... Which leads where??

    c) If, after (b), you then encode
    01 --> 0
    011 --> 1
    do you recover the same one??

    Reencodings like these are not the only approach...

    ReplyDelete
  3. Anonymous12:54 PM

    Does the sequence repeat?

    ReplyDelete
  4. Clearly, it is very repetitious. It absolutely never repeats.

    ReplyDelete