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:

5) Etc.: ...

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)?


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

    huhu im confused..

  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...

  3. Anonymous12:54 PM

    Does the sequence repeat?

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