Talk:Palindromic number

What about 196?

I assume you're talking about the status of 196 as the smallest (suspected) Lychrel number? It's discussed in that article, although I've added a link to it here in the "see also" section. Chuck 15:33, 31 October 2005 (UTC)

Infinitely many

I know it's obvious, but I think it should be stated that in any given base there are infinitely many palindromic numbers. So I've added that in the top section. I don't really have any feelings about where in the article it should go, though, so move it elsewhere in the article if you want. Hammerite 01:05, 2 March 2006 (UTC)

Percentage

What is the percentage of all numbers that are palindromic?

0%--as the number of digits grows larger, the fraction of those numbers which are palindromic grows smaller, approaching 0% as the number of digits goes to infinity. For example:

Number of digits	Range of numbers	Total numbers in range	Palindromic numbers in range	Fraction of palindromic numbers in range	Cumulative range	Cumulative total numbers	Cumulative palindromic numbers	Cumulative fraction
1	0-9	10	10	1	0-9	10	10	1
2	10-99	90	9	0.1	0-99	100	19	0.19
3	100-999	900	90	0.1	0-999	1000	109	0.109
4	1000-9999	9000	90	0.01	0-9999	10000	199	0.0199
5	10000-99999	90000	900	0.01	0-99999	100000	1099	0.01099
6	100000-999999	900000	900	0.001	0-999999	1000000	1999	0.001999

To be more general, the number of palindromic numbers in base b with n digits is:

${\begin{cases}b,&n=1\\(b-1)b^{\left\lfloor {\frac {n-1}{2}}\right\rfloor },&n>1\end{cases}}$

where $\left\lfloor x\right\rfloor$ is the floor function (the floor function in that formula is the exponent of b, even though that's not too clear the way it's represented here).

And the fraction of numbers in base b with n digits which are palindromic is:

${\frac {1}{b^{\left\lfloor {\frac {n-1}{2}}\right\rfloor }}}$

The fraction of numbers in base b with n or fewer digits which are palindromic is:

${\frac {b^{\left\lfloor {\frac {n+1}{2}}\right\rfloor }+b^{\left\lfloor {\frac {n}{2}}\right\rfloor }-1}{b^{n}}}$

which approaches zero as n goes to infinity.

This is all original research, of course, so it can't go in the article itself unless an outside source can be found for it. Chuck 15:31, 8 March 2006 (UTC)

Bananan vhgdfjhfjdfdkjjdfhjdfhd    

ur a bigg fatty

Convertion

I added a method of converting non-palindromic numbers to palindromic numbers. Hopefully the informtion is useful, but if it should be deleted, then I'm sorry...Littleghostboo[ talk ] (Win an argument and leave your mark in history.) 09:08, 29 April 2007 (UTC)

Is convertion a math word? I didn't find it on dictionary.com or in wikipedia. Should this heading be conversion instead?