Edwin Clark eclark at math.usf.edu
Sat May 24 19:01:59 CEST 2003

```On Sat, 24 May 2003, N. J. A. Sloane wrote:

>
> %I A083960
> %S A083960 1,2,3,4,5,6,7,8,9,10,11,2112,313313,4441444,5115,61616
> %N A083960 Smallest palindromic multiple (ignoring leading zeros) of n using only and all digits of n; or 0 if no such number exists.
> %C A083960 Conjecture: No entry is zero.
> %Y A083960 Cf. A083961.
> %O A083960 1,2
> %K A083960 base,more,nonn
> %A A083960 Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), May 20 2003
>

Having 10, 20, etc., count as palindromes is unfortunate but unavoidable
in this case. Neverless it is fun trying to extend the sequence. I get the
following extension:

7111117, 8118, 99199, 20, 1121211, 22, 32223, 4224, 525, 262262,
722277772227, 828828, 922229, 30

Here are the factorizations:

17*418301 = 7111117
18*451=8118
19*5221=99199
20*1=20
21*53391=1121211
22*1=22
23*1401=32223
24*176=4224
25*21=525
26*10087=262262
27*26751028601=722277772227
28*29601=828828
29*31801=922229
30*1=30

---Edwin Clark

```