What is the name of this type of palindromic number?

Question

A palindromic number is one that reads the same forwards as backwards, an example of which is $17071$.

In the UK yesterday's date was $16/3/16$, the convention being day/month/year. Clearly $16316$ is not palindromic in the usual sense. However if you swap the day with the year it still is $16316$. This a kind of 'block' palindrome whereby you can swap number blocks. Another example is $26726$ here you can swap the $26$ around.

Is there a name for such 'palindromic' numbers?

I had a look on the internet but didn't find anything obvious as the problem seems linked to which base the number is written in.

Thanks in advance.

Answer 1

As of $2018$ there is a name that was used in a paper, "Block palindromes", in "Block Palindromes: A New Generalization of Palindrome, Keisuke Goto."

• Links: Arxiv.org / Springer.com / Researchgate.net.

Where they use the following definition:

A block palindrome is a string that becomes a palindrome when identical substrings are replaced with a distinct character.

In the paper, they give an example of "block factorization": To|kyo|_|and|_|Kyo|to (page 2).

For example, your $16316$ is a block palindrome with blocks ("block factorization"): $16|3|16$.