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        riddles >> medium >> find
        
(Message started by: tony123 on Jul 7^th, 2007, 3:43pm)

Title: find
Post by tony123 on Jul 7^th, 2007, 3:43pm

http://www.sosmath.com/CBB/latexrender/pictures/aa1c1da929c9347fddda5d32bb20d5e5.gif

Title: Re: find
Post by denis on Jul 7^th, 2007, 5:59pm

[hide]n=1: 1/2
n=2: 3/8
n=3: 21/64
n=4: ~~315/256~~ 315/1024
.
.
.

So we have basically two sequences to figure out

The denominators 2,8,64, 1024 ... which is ~~2²ⁿ~~ ~~2^2n-1~~
2^n(n+1)/2

and the sequence of nominators

1,3,21,315,... which is the 2 factorial sequence:
(1, 1*3, 1*3*7, 1*3*7*15, ...

=[n]₂! as shown in:

http://www.emis.de/journals/JIS/VOL9/Morrison/morrison37.pdf

So we get for general n: ~~[n]₂!/2^2n-1~~
[n]₂!/2^n(n+1)/2

[/hide]

EDIT: Thanks to Fibster for finding my erroneous calculations.

Title: Re: find
Post by FiBsTeR on Jul 7^th, 2007, 6:56pm

on 07/07/07 at 17:59:15, denis wrote:

The denominators 2,8,64,256 etc which is 2²ⁿ

Ummm, maybe I'm doing something wrong, but 2²ⁿ = 4ⁿ which is {4,16,64,256,...}.

Title: Re: find
Post by denis on Jul 7^th, 2007, 7:01pm

Ooops. Went too fast.

2,8,64,256 = 2²ⁿ/2=2^2n-1

Thanks for pointing out my error ...

Corrected in my post above...

Title: Re: find
Post by FiBsTeR on Jul 7^th, 2007, 7:06pm

on 07/07/07 at 19:01:40, denis wrote:

2,8,64,256 = 2²ⁿ/2=2^2n-1

I think you're still going too fast! :-/

2²ⁿ/2 = 4ⁿ/2, which is {2,8,32,128,...}

Title: Re: find
Post by denis on Jul 7^th, 2007, 7:11pm

Darn... Your right :(

the correct seqence for the denominators is 2,8,64,1024, ...

how about

2, 8, 64, 1024 ... = 2^n(n+1)/2

Corrected again in post above...

8)

Title: Re: find
Post by FiBsTeR on Jul 7^th, 2007, 7:20pm

Now you're thinking too much and you've completely overstepped the problem! Remember, you're trying to find a sequence for {2,8,64,256,...} and not {2,8,64,1024,...}

And BTW, if someone comes along thinking they'll use that encyclopedia for integer sequences, don't bother (http://www.research.att.com/~njas/sequences/?q=2%2C8%2C64%2C256&sort=0&fmt=0&language=english). :P

EDIT:
Nevermind, I misread the post.