[seqfan] Enough palindromes

[Eric Angelini]

Hello SeqFans,
based on the same idea, but looking to the left:

S=1,11,21,2,12,22,32,3,13,23,33,43,4,14,24,34,44,54,5,15,25,35,45,55,65,6,16,...
 
Start with a(1)=1 and extend S with the smallest unused integer
such that a(n+1) concatenated to the rightmost digit of a(n), or
to the 2-rightmost digits of a(n), or to the 3-rightmost digits
of a(n), or... shows a palindrome.

Example:
1 and 11 show "111"
11 and 21 show "121"
21 and 2 show "212"
2 and 12 show "212"
12 and 22 show "222"
22 and 32 show "232"
32 and 3 show "323"
3 and 13 show "313"
13 and 23 show "323"
...

Question: for which "n" shall we have a(n)=10?
Best,
É.