You’re Not Trying

I few days back I inked a post about Douglas Hofstadter’s fascinating book Gödel, Escher, Bach: An Eternal Golden Braid, in which I showed a little item from the chapter Figure and Ground, which is about recursively enumerable systems. The tidbit I offered was a most unusual number series. Here it is again, for those of you who didn’t see it the first time around, or who just passed it by without really thinking about it:

1   3   7   12   18   26   35   45   56   69 …

I admit it takes a minute or two to make sense of it, but it is worth the effort. It is wonderfully strange, and is typical of the little jewels that are everywhere in that amazing book.

And don’t worry, I am not going to make a habit of posting retreads.

Related content from Sphere

13 Comments

  1. Thomas says

    I have tried now for a few minutes, but I don’t get it… :o/ I’m not too good at these kind of puzzles, and patience is not my best friend.

    Posted January 13, 2006 at 5:43 am | Permalink
  2. eugene says

    Let A(N) be a sequence 1 3 7 12 18 26 35 45 56 69 …
    A(0) = 1, A(1) = 3 and so on.
    defined C(N) = A(N+1) – A(N)
    we get C(N) as 2 4 5 6 8 9 10 11 …..
    So C(N) can be defined as the sequence in natural number sequence that are not
    A(N),
    Then A(N) = A(N-1) + C(N).

    [Note: Eugene Jen had posted a C++ snippet here that would generate the sequence, but asked me to withdraw it, as it needs a little work. Check back later. -Malcolm]

    Posted January 13, 2006 at 8:19 am | Permalink
  3. Thomas says

    ehh, well okay, so it’s not that simple…. :o)

    Posted January 13, 2006 at 8:52 am | Permalink
  4. Malcolm says

    Hi Thomas,

    No, the concept is quite simple! You have to understand that my friend Eugene is a mathematician and computer scientist, and skipped right past the simple natural-language rule to a rigorous treatment of the generation algorithm. Click here for a much clearer description.

    Posted January 13, 2006 at 10:37 am | Permalink
  5. the one eyed man says

    I am still working on the number sequence, but I can offer several puzzles of a different nature. Living in Silicon Valley, you typically see license plates like 2DOT0 or (on a Porsche) 300SHRS. Today’s puzzles are my favorite plate (JPGANDR) and my favorite bumper sticker (STFU and drive).

    Posted January 13, 2006 at 11:59 am | Permalink
  6. Malcolm says

    Hi Peter,

    Well, I assume that “2DOT0” refers to a software or protocol version, and would hazard guesses that “300SHRS” might belong to someone who was prescient enough to have bought some Google stock, that “JPGANDR” refers to a certain mop-topped Liverpudlian foursome, and that “STFU and drive” is an exhortation to attend to one’s vehicular responsibilities in a tight-lipped fashion.

    How’d I do?

    Posted January 13, 2006 at 12:06 pm | Permalink
  7. the one eyed man says

    A plus

    Can you take my SAT’s for me?

    Posted January 13, 2006 at 1:08 pm | Permalink
  8. Malcolm says

    I have absolutely no idea what you could possibly be referring to.

    Posted January 13, 2006 at 1:36 pm | Permalink
  9. Kevin Kim says

    It’s still Greek to me, even with the explanation. The way I read it, the explanation is saying, “The numbers you don’t see in the sequence are not in the sequence,” which is tautological and unhelpful if I want to know the next few numbers in the sequence.

    What am I doing wrong here?

    Much easier to understand is “the one eyed man’s” expression, “A plus,” which is how young French folks sign their emails to each other. They usually write “A plus” in French l33tsp33k as “A+,” a shortened form of “à plus tard,” or “later.”

    Kevin

    Posted January 18, 2006 at 8:09 am | Permalink
  10. Malcolm says

    Hi Kevin,

    I’ve added to the explanatory note. Take another look!

    -Malcolm

    Posted January 18, 2006 at 10:43 am | Permalink
  11. Kevin Kim says

    I’m terrible with finding such patterns. That’s pretty amazing.

    Thanks,

    Kevin

    Posted January 19, 2006 at 12:34 am | Permalink
  12. Andrew says

    Thanks, I’ve been puzzling over it. I had all the information, just didn’t connect the dots (I had calculated the difference between the numbers in the sequence, but it just never triggered that those were the same numbers that were NOT in the sequence). Extremely clever sequence :) Thanks for puzzling it out and sharing!

    Posted December 27, 2006 at 6:01 am | Permalink
  13. Malcolm says

    Hi Andrew, and welcome!

    I think you now have the current record for commenting on the oldest over-the-horizon post.

    Posted December 27, 2006 at 12:23 pm | Permalink