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# Demlo number

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

The Demlo numbers for $n<b$ are also palindromic numbers, and specifically of the form

$nb^{{n-1}}+\sum_{{i=1}}^{{n-1}}(ib^{{2n-i}}+ib^{{i-1}}),$ |

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.

Synonym:

wonderful Demlo number

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

11A63*no label found*

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