Monday, September 08, 2008

Three sequences

Here are three finite sequences. There is no next element, I give you the complete sequence. What rule did I use to form these sequences?
  1. 8,5,4,9,1,7,6,3,2
  2. 8,5,1,4,9,2,7,6,3
  3. a,i,s,e,t,d,m,c,o,l,p,n,x,v,b,w,y,f,r,u,k,g,z,h,j,q


  1. Sequence 1 seems to be the the numbers 1-9 in English alphabetical order. It is even listed as such in Sloane's, but I already knew this `riddle' from highschool. (Though in Holland it is 8 3 1 9 2 4 5 6 7, for ``acht drie een negen twee vier vijf zes zeven'')
    Second one doesn't show up in Sloane.

  2. Only 1 and 2 moved...


  3. Second sequence is ordinals alphabetized, just as first sequence is cardinals alphabetized.

  4. Third sequence looks vaguely like letter frequencies, although if it is, either the source text is really odd or the language isn't English... possibly Esperanto?

  5. Since these are finite sequences, I can always fit a polynomial and there is nothing more significant than that.

    So, no matter what rule you chose to generate them I can interpret that rule as a polynomial function and nothing more.

  6. First sequence is indeed
    the numbers in alph order.
    Second sequence is indeed
    the ordinals in alph order.
    The third sequence is
    sortof freq-- I typed
    a, b, c, ... into google
    and this is the number of
    hits in order.

    YES, any finite sequence
    has some poly that generates it. I was looking
    for the ``best explanation''. Not sure
    that can be rigorously defined, perhaps with
    Kolg theory.

  7. The 3rd is pretty close to the count of results from Google. It is worth noting that since that's a moving target it doesn't make a great question. Right now, Google is reporting more results for o then c and more for b then v, and I only checked half the letters.

  8. What I'm curious about is this: say you type numbers at random and ask people to "explain" the sequence. What kind of answers would people come up with?