Demlo number

Given base $b$, a number of the form ${(\frac{b^n-1}{b-1})}^2$ for $n>0$ (that is, the square of a repunit) is a Demlo number, sometimes called a wonderful Demlo number.

The Demlo numbers for are also palindromic numbers, and specifically of the form

$$n{b}^{n-1}+\sum _{i=1}^{n-1}(i{b}^{2n-i}+i{b}^{i-1}),$$

that is, the most significant digits are the first $n$ digits of base $b$ in order and the least significant digits are the first $n$ digits of base $b$ backwards.