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#1 2006-01-15 04:37:40

krisper
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Really cool thing with the numbers like a^x

Here is what we do:
1. We have the numbers from 1 to 10 a∈{1,2,3,4,5,6,7,8,9,10}.
2. x is the power of these numbers.
3. Take any random integer number x that is between 0 and +∞.
4. Calculate
1^x = b1
2^x = b2
3^x = b3
4^x = b4
5^x = b5
6^x = b6
7^x = b7
8^x = b8
9^x = b9
10^x = b10
5. Now the fun part smile We calculate this:
c1 = b2 - b1;
c2 = b3 - b2;
c3 = b4 - b3;
c4 = b5 - b4;
c5 = b6 - b5;
c6 = b7 - b6;
c7 = b8 - b7;
c8 = b9 - b8;
c9 = b10 - b9;
6. Now we have the set of numbers c1..c9. We do the same and get the set d1..d8 (d1 = c2 - c1, d2 = c3 - c2 and etc.). We do this until we get a set of numbers that has equal numbers and if we decide to subtract again we will get 0. These equal numbers we will call Z.
7. Write here what value of x have you used and what Z have you got as answer?


P.S.
If all your calculations are correct you will have a Z that equals x! smile

Last edited by krisper (2006-01-15 07:47:46)


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#2 2006-01-15 05:06:29

mathsyperson
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Re: Really cool thing with the numbers like a^x

That only works when x is a positive integer.

It's a nice pattern though. I played around with it, and discovered that you need to do Step 4. x times before you get your Z value. Also, if you're doing high values of x, you'll need more than 10 numbers to start off with.

Last edited by mathsyperson (2006-01-15 10:28:29)


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#3 2006-01-15 06:12:52

krisper
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Re: Really cool thing with the numbers like a^x

Thanks for your reply mathsyperson.

And yes, you are correct and  that why I said that x should be >=0 smile By the way I found this on my own a couple of years ago when I was playing of numbers hoping I will find something significant (everyone's dream smile ). It is very nice though, because when repeating the steps you will always get to the 0 value.


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#4 2006-01-15 06:31:17

mathsyperson
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Re: Really cool thing with the numbers like a^x

It doesn't work with x=0 either. For that, you get a Z value of 1.
And my main point in the previous post was that x had to be an integer. If you take it as √ 2, then you'll get all kinds of odd numbers. They won't ever reach 0 either. At least, I don't think they will.


Why did the vector cross the road?
It wanted to be normal.
 

#5 2006-01-15 07:20:36

krisper
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Re: Really cool thing with the numbers like a^x

When is 0 you will get Z=1 and 0! equals 1, so n can be 0 smile And you are right again, it is only for integers because n! formula can only be used for integers that are >=0.

P.S. I have edited my first post telling that x must be integer smile

Last edited by krisper (2006-01-15 07:48:45)


Humankind's inherent sense of right and wrong cannot be biologically explained.
 

#6 2006-01-15 09:45:52

MathsIsFun
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Re: Really cool thing with the numbers like a^x

From Excel:

Code:

        
x=4        
        
 1        1                    
 2       16      15                
 3       81      65     50            
 4      256     175    110     60        
 5      625     369    194     84    24    
 6     1296     671    302    108    24    0
 7     2401    1105    434    132    24    0
 8     4096    1695    590    156    24    0
 9     6561    2465    770    180    24    0
10    10000    3439    974    204    24    0

And for x=5 you need an extra column to reach 0

And it is fun to play with real values of x


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#7 2006-01-15 10:31:08

mathsyperson
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Re: Really cool thing with the numbers like a^x

krisper wrote:

When is 0 you will get Z=1 and 0! equals 1, so n can be 0 smile

Oh! Sorry! When I read your original thing about Z=x!, I inferred that that was an exclamation mark, but now after reading MathsIsFun's post I realise that it was actually a factorial sign. Sorry again! rolleyes


Why did the vector cross the road?
It wanted to be normal.
 

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