# Product of repunits = palindromes : another old hat?!

Maximilian Hasler maximilian.hasler at gmail.com
Wed Apr 4 17:30:25 CEST 2007

```Dear Zakir,
the square of Rm = (10^m-1)/9 is just a particular case of Rm*Rn,
palindromic for min{m,n} < 10 since Rn=10^(n-1)+...+1 and thus Rm*Rn =
11...11*Rn
= 11...11000...0
+  11...1100...0
+   11...110...0
+...+   11...110
+        11...11
= 123........321.

-M.H.

On 4/4/07, Zakir Seidov <zakseidov at gmail.com> wrote:
> Dear seqfans,
>
> It's known that R(n)^2 (n=1..9) (square of repunits) are palindromes,
> but is it old hat that
> R(n)*R(m) (n=1..9) for ANY m are  also palindromes   ?!
>
> Zak
>
> ta12=Table[(10^k-1)/9 (10^(k+12)-1)/9,{k,9}]
> IntegerDigits[#]==Reverse[IntegerDigits[#]]&/@ta12
> {1111111111111,122222222222221,12333333333333321,1234444444444444321,123455555555555554321,12345666666666666654321,1234567777777777777654321,123456788888888888887654321,12345678999999999999987654321}
> {True,True,True,True,True,True,True,True,True}
>
> Weisstein, Eric W. "Demlo Number" ,
> http://mathworld.wolfram.com/DemloNumber.html
> A002275, A002477, A080151, A080161, and A080162
>

```