> Can a natural number $n$ be *nontrivially* [palindromic](https://en.wikipedia.org/wiki/Palindromic_number) in more than $3$  consecutive integer bases? 
> 
> *Nontrivially* means that I'm not counting one-digit palindromes.

The [initial question was asked on Math.SE](https://math.stackexchange.com/questions/2234587/can-a-number-be-palindrome-in-4-consecutive-number-bases)  and holds all the *progress* so far - it references the $3$-digit patterns, but it seems that the exceptions appearing among them prevent a full analysis of the patterns and thus the question remains **unsolved**.

By posting here, I'm hoping to find out If there is any other mathematical way to tackle a problem like this one?