Silliest series
 

It seems puzzles of series are welcome.Here is the silliest one 8) :
1
11
21
1211
111221
.........??? :?
In fact it's really silly.(more than you can imagine ;) )

312211
13112221
1113213211
31131211131221
13211311123113112211
11131221133112132113212211
3113112221232112111312211312112211
13211321321112131221123113112221131112212221
1113122113121113123112111311222112132113213221133122113211

8)

Seems to be a new kind of formula for a parabolic curve

Seems to be this rule, parsing from the left:

1 -> 11
11 -> 21
2 -> 12

so,
1
11
21
1211
111221
2111121211
12212112111221

Oh, geez. It's a word rule.

1
"one one" - 11
"two ones" - 21
"one two, one one" - 1211
"one one, one two, two ones" - 111221
"three ones, two twos, one one" - 312211
etc. ... meaning I agree with koal

It is known as Conway "Look and say" sequences.

John Horton Conway described a "cosmological theorem based upon these series.

http://mathworld.wolfram.com/CosmologicalTheorem.html
http://www.math.lsu.edu/~lither/jhc/

Also notice that such series find out a "constant" called Conway constant"

http://mathworld.wolfram.com/ConwaysConstant.html

Finally, each number sequence may be studied at

http://www.research.att.com/~njas/sequences/Seis.html

Regards :-)

Luigi

:surprised: :surprised: :surprised: SO MUCH RESEARCH ON THIS！！！！！
I just thought it's a funny puzzle ;)

Edit: On second thought, never mind.

Cheesehead...

Well, never mind :-D

Luigi