Anything Special About 495 and 6174
Step 1:
If you take any three digit number excluding the ones with 3 same
digits , say you choose 512.
Step 2:
Then you rearrange this number to get the maximum and minimum number
represented by these digits which will be 521 and 125 respectively.
Subtracting the smallest from the largest would yield 396
You now repeat Step 2 with the number you had from subtraction
963 - 369=594
Back to Step 2:
954-459=495
If you try these steps with any three digit number, given that all
three digits are not same; you will end up with 495 if you go through
the procedure in step 2.
For four digit numbers, the process terminates at 6174
The procedure does not terminate at any special number for numbers
with more than 4 digits
Website: http://www.BritishComputerColleges.com/VU/polaRgraphs.html
date: Sat, 14 Jul 2007 10:42:17 -0700
author: DexterOnline
|
Re: Anything Special About 495 and 6174
On Sat, 14 Jul 2007 19:42:17 퍭, DexterOnline wrote:
> The procedure does not terminate at any special number for numbers
> with more than 4 digits
The numbers /are/ special, they are the 2nd and 3rd term of the Kaprekarmapping. The sequence starts as follows: 0, 495, 6174, 549945, 631764, .Check the Kaprekar mapping at
http://www.research.att.com/~njas/sequences/A099009
Regards,
//Herbert
-- 0.7 = [0; 1, 2, 3]
http://herbert.gandraxa.com/herbert/cfr.asp
date: Tue, 20 Nov 2007 17:08:41 +0100
author: Herbert Glarner
|