Computational Complexity and other fun stuff in math and computer science from Lance Fortnow and Bill Gasarch
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.
Only 1 and 2 moved...8th,5th,1st,4th,9th,2nd,7th,6th,3rd.
Second sequence is ordinals alphabetized, just as first sequence is cardinals alphabetized.
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?
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.
First sequence is indeedthe numbers in alph order.Second sequence is indeedthe ordinals in alph order.The third sequence is sortof freq-- I typeda, b, c, ... into googleand this is the number of hits in order.YES, any finite sequencehas some poly that generates it. I was lookingfor the ``best explanation''. Not surethat can be rigorously defined, perhaps withKolg theory.
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.
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?