Repdigit

Repdigit Triangular Numbers [article title]

Is there any system of notation in which there is a repdigit aa such that (aa)²#61;ccdd, with c#61;a-1 and d#61;c-1?

Here is another palindromic magic square that has the added property of having main diagonals containing eight repeating "repdigits": 222, 333, 444, 555, 666, 777, 888, and 999. The magic sum is 2442.

A positive with repeated digit is called a repdigit, for example 222, 55555, and all repunits are repdigits.