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.

Title	Demlo number
Canonical name	DemloNumber
Date of creation	2013-03-22 16:22:01
Last modified on	2013-03-22 16:22:01
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	5
Author	PrimeFan (13766)
Entry type	Definition
Classification	msc 11A63
Synonym	wonderful Demlo number