I think for the purposes of this, you must take 0 as even. And starting at zero gives exactly the same result as 2,4,6,8 - you get 101 213 123
With the number 1: 011 213 123 On 4/29/05, Abinanthan.B <[EMAIL PROTECTED]> wrote: > > > > IS 0 A EVEN NUMBER? > > > > WHAT IF I TAKE THE STRATING NUMBER ITSELF AS "0"? > > > > ________________________________ > > > From: [email protected] [mailto:[EMAIL PROTECTED] On Behalf > Of vijay gopinath > Sent: 29 April 2005 12:39 > To: [email protected] > Subject: RE: [tech4all] MATHEMATICAL BLACK HOLE > > > > > > 222 ----- > > > No: of even numbers - 3 > > > No: 0f Odd numbers - 0 > > > Total number - 3 > > > Therefore 303 -----That leads to again > > > No of even Numbers -1 > > > No of odd numbers -2 > > > Total number - 3 > > > Therefore "123 " > > > > > > Same with 4 too > > > > > > Thanks , > > > > > > Vijay > > "Abinanthan.B" <[EMAIL PROTECTED]> wrote: > > > what about 222 or 4? > > -----Original Message----- > From: [email protected] > To: [email protected]; [EMAIL PROTECTED]; > [EMAIL PROTECTED] > Sent: 28/04/2005 15:36 > Subject: [tech4all] MATHEMATICAL BLACK HOLE > > Whhhhattt? Black hole in maths? > Yup.. In maths a black hole is a number to which an > operation on any of the elements of UNIVERSAL set > finally leads to... figuratively speaking everything > "BOILS DOWN TO THAT ELEMENT.." > > The following are two of the mathematical BLACK > HOLES... > > The Sisyphus String: 123 > > Suppose we start with any natural number, regarded as > a string, such as 9288759. Count the number of even > digits, the number of odd digits, and the total number > of digits. These are 3 (three evens), 4 (four odds), > and 7 (total of seven digits). So, use these digits to > form the next string or number, 347. > > Now repeat with 347, counting evens, odds, total > number, to get 1, 2, 3, so write down 123. If we > repeat with 123, we get 123 again. The number 123 with > respect to this process and universe of numbers is a > mathemagical black hole. All numbers in this universe > are drawn to 123 by this process, never to escape. > > Will every number really be sent to 123? Try > > 122333444455555666666777777788888888999999999. > > The numbers of evens, odds, and total are 20, 25, and > 45, respectively. So, our next iterate is 202545, the > number obtained from 20, 25, 45. Iterating for 202545 > we find 4, 2, and 6 for evens, odds, total, so we have > 426 now. One more iteration using 426 produces 303, > and a final iteration from 303 produces 123. > > Narcissistic Numbers: 153 > > It is well known that, other than the trivial examples > of 0 and 1, the only natural numbers that equal the > sum of the cubes of their digits are 153, 370, 371, > and 407. Of these, only 153 has a black-hole property. > To create a black hole, we need to define a universe > (set U) and a process (function f). We start with any > positive whole number that is a multiple of 3. Recall > that there is a shortcut to test whether you have a > multiple of 3. Just add up the digits and see whether > that sum is a multiple of 3. For instance, 111111 (six > ones) is a multiple of 3 because the sum of the > digits, 6, is. However, 1111111 (seven ones) is not. > Since we are going to be doing some arithmetic, you > may wish to take out a hand-calculator and/ or some > paper. Write down your multiple of 3. One at a time, > take the cube of each digit. Add up the cubes to form > a new number. Now repeat the process. You must > eventually reach 153. Moreover, once you reach 153, > another iteration just gets you 153 again. > > Let's test just one initial instance. Using the sum of > the cubes of the digits, if we start with 432 - a > multiple of 3 - we get 99, which leads to 1458, then > 702, which yields 351, finally leading to 153, at > which point, future iterations keep producing 153. > Note also that this operation or process preserves > divisibility by 3 in the successive numbers. > > __________________________________ > Do you Yahoo!? > Yahoo! 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