The palindromes of length 1 are 0,1,…,9.

Let 𝑛 be a positive even integer; let 𝑛=2𝑚. Every palindrome of length 𝑛 is of the form
∑𝑘=0𝑚−1𝑝𝑘(10(𝑛−1)−𝑘+10𝑘)
where 𝑝0,𝑝1,…,𝑝𝑚−1∈{0,1,…,9}, 𝑝0≠0.

Let 𝑛 be a positive odd integer, 𝑛≥3; let 𝑛=2𝑚+1. Every palindrome of length 𝑛 is of the form
∑𝑘=0𝑚−1𝑝𝑘(10(𝑛−1)−𝑘+10𝑘)+𝑝𝑚10𝑚
where 𝑝0,𝑝1,…,𝑝𝑚∈{0,1,…,9}, 𝑝0≠0.