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.

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?

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.

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?

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'')

ReplyDeleteSecond one doesn't show up in Sloane.

Only 1 and 2 moved...

ReplyDelete8th,5th,1st,4th,9th,2nd,7th,6th,3rd.

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

ReplyDeleteThird 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?

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

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

First sequence is indeed

ReplyDeletethe 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.

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.

ReplyDeleteWhat 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?

ReplyDelete