0, 1, 2, 720!
Patrick Crotty
1!!!, 2!!!, 3!!!, and that the next entry would be 4!!!. But
what about 0? I've always seen 0! defined as 1, not 0, and so
unless I'm completely missing something, the original puzzle
should have been called 1, 1, 2, 720!. It seems to me that
a more correct solution, if 0 is to be included, would be
0, 1!, 2!!, 3!!!, and so the next entry would be 4!!!!, not 4!!!.
Agai, though, I'm not sure about this, so please tell me if
I'm wrong.
Patrick Crotty
p...@physics.wm.edu
Jan Ritsema van Eck
>From: p...@physics.wm.edu (Patrick Crotty)
>Subject: Re: 0, 1, 2, 720!
>Date: Tue, 18 Apr 1995 23:30:52 GMT
>Some said that this is the sequence
>1!!!, 2!!!, 3!!!, and that the next entry would be 4!!!. But
Make that 1!!, 2!!, 3!! (3! = 6, 6! = 720; of course for 1 and 2 the number
of !'s doesn't make any difference)
>what about 0? I've always seen 0! defined as 1, not 0, and so
That's what bothered me, too
>unless I'm completely missing something, the original puzzle
>should have been called 1, 1, 2, 720!. It seems to me that
>a more correct solution, if 0 is to be included, would be
>0, 1!, 2!!, 3!!!, and so the next entry would be 4!!!!, not 4!!!.
No. See above, 3!!! = 720! (a number I am not going to compute).
^this is a mathematical '!', not a punctuation mark
Still puzzled. What did we miss?
Seth Breidbart
Jan Ritsema van Eck <j.ri...@frw.ruu.nl> wrote:
>In article <1995Apr18....@cs.wm.edu> p...@physics.wm.edu (Patrick Crotty) writes:
>>From: p...@physics.wm.edu (Patrick Crotty)
>>Some said that this is the sequence
>>1!!!, 2!!!, 3!!!, and that the next entry would be 4!!!. But
>Make that 1!!, 2!!, 3!! (3! = 6, 6! = 720; of course for 1 and 2 the number
>of !'s doesn't make any difference)
No, you _want_ 720!.
>>what about 0? I've always seen 0! defined as 1, not 0, and so
>That's what bothered me, too
>>unless I'm completely missing something, the original puzzle
>>should have been called 1, 1, 2, 720!. It seems to me that
>>a more correct solution, if 0 is to be included, would be
>>0, 1!, 2!!, 3!!!, and so the next entry would be 4!!!!, not 4!!!.
>No. See above, 3!!! = 720! (a number I am not going to compute).
> ^this is a mathematical '!', not a punctuation mark
>Still puzzled. What did we miss?
The last character in the Subject: header?
Seth
David Karr
>In article <1995Apr18....@cs.wm.edu> p...@physics.wm.edu (Patrick Crotty) writes:
>>From: p...@physics.wm.edu (Patrick Crotty)
>Make that 1!!, 2!!, 3!! [...]
>
>>a more correct solution, if 0 is to be included, would be
>>0, 1!, 2!!, 3!!!, and so the next entry would be 4!!!!, not 4!!!.
>
>No. See above, 3!!! = 720! (a number I am not going to compute).
See above indeed. I see 720! following 2 in the sequence. I do not
see 3!! = 720 in the sequence.
In any case, 0!! = 1, so where did the initial 0 come from? It's the
initial 0 that causes people to guess 0, 1!, 2!!, 3!!!, 4!!!! rather
than any of the sequences with a constant number of apllications of
factorial.
-- David A. Karr (ka...@cs.cornell.edu)
Dave Ring
>initial 0 that causes people to guess 0, 1!, 2!!, 3!!!, 4!!!! rather
>than any of the sequences with a constant number of apllications of
>factorial.
Another reasonable possibility for the next number is (720!+1)!!!
--
Dave Ring
dwr...@tam2000.tamu.edu
Philip Gibbs
>>
> In any case, 0!! = 1, so where did the initial 0 come from? It's the
> initial 0 that causes people to guess 0, 1!, 2!!, 3!!!, 4!!!! rather
> than any of the sequences with a constant number of apllications of
> factorial.
>
or perhaps its generated recursively from
x -> (x+1)!!
or, depending on how you interpret the ! in the sequence
x -> (x+1)!!!
so the next number is 721!! or (720!+1)!!!