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From: Nilnod on 27 Jan 2006 07:14

Palindromic number is a number that reads the same backward or forward
like 1991 ...
Or if a number is not palindromic it can lead to a palindromic number
after several iterations.
For example, take 25,
Reverse it that makes 52 and then add which will make 77 which is again
palindromic.

It is interesting to note that a number ,say, 196 can never lead to
palindrimic number after infinite iteration also - why this is so?
Santosh

From: Jerry Avins on 27 Jan 2006 10:49
Nilnod wrote:
> Palindromic number is a number that reads the same backward or forward
> like 1991 ...
> Or if a number is not palindromic it can lead to a palindromic number
> after several iterations.
> For example, take 25,
> Reverse it that makes 52 and then add which will make 77 which is again
> palindromic.
>
> It is interesting to note that a number ,say, 196 can never lead to
> palindrimic number after infinite iteration also - why this is so?
> Santosh

There is a carry when the addition is made.

Jerry
--
Engineering is the art of making what you want from things you can get.
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From: No Never on 27 Jan 2006 10:49
Dear Santosh,

Why not transforming 196 from the decimal system to a system
with the basis 4 ?
Hence, 196d will become 3*64+0*16+1*4+0*1 = 3010q.
If you now make your "iteration"
Reverse it that makes 103q. and then add which will make 3113q.
Isn't this a nice palindromic number ?

Regards, Wolfgang

P.S.: I like 196, it's not fair to say one couldn't make it "palindromic".
:-)
But could evey number be made palindromic that way ?



From: Raymond Toy on 27 Jan 2006 12:03
>>>>> "Jerry" == Jerry Avins <jya(a)ieee.org> writes:

Jerry> Nilnod wrote:
>> Palindromic number is a number that reads the same backward or forward
>> like 1991 ...
>> Or if a number is not palindromic it can lead to a palindromic number
>> after several iterations.
>> For example, take 25,
>> Reverse it that makes 52 and then add which will make 77 which is again
>> palindromic.
>> It is interesting to note that a number ,say, 196 can never lead to
>> palindrimic number after infinite iteration also - why this is so?
>> Santosh

Jerry> There is a carry when the addition is made.

47 + 74 = 121. What carry are you talking about?

This is a pretty famous problem. The iteration can be done for just
about every number and you'll eventually get a palindrome. But 196
doesn't seem to work. I don't know if anyone has actually proven that
the iteration fails for 196.

Ray
From: Jani Huhtanen on 27 Jan 2006 12:17
Jerry Avins wrote:

> Nilnod wrote:
>> Palindromic number is a number that reads the same backward or forward
>> like 1991 ...
>> Or if a number is not palindromic it can lead to a palindromic number
>> after several iterations.
>> For example, take 25,
>> Reverse it that makes 52 and then add which will make 77 which is again
>> palindromic.
>>
>> It is interesting to note that a number ,say, 196 can never lead to
>> palindrimic number after infinite iteration also - why this is so?
>> Santosh
>
> There is a carry when the addition is made.
>

Yes, but at least for me it is not clear that for every iteration there will
be (or will not be) carry when the addition is made.

For the first five there seems to be carry and thus the additions do not
lead to palindromic numbers:
196 -> 887 -> 1675 -> 7436 -> 13783 -> ...

--
Jani Huhtanen
Tampere University of Technology, Pori
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