Definition:Repunit

Definition

Let $b \in \Z_{>1}$ be an integer greater than $1$.

Let a (positive) integer $n$, greater than $b$ be expressed in base $b$.

$n$ is a repunit base $b$ if and only if $n$ is a repdigit number base $b$ whose digits are $1$.

That is, $n$ is a repunit base $b$ if and only if all of the digits of $n$ are $1$.

When $b$ is the usual base $10$, $n$ is merely referred to as a repunit.

Index

The index of a repunit is the number of digits it has.

Thus a repunit with $n$ digits can be referred to as $R_n$.

Also see

• Definition:Repunit Prime

• Results about repunits can be found here.

Historical Note

According to David Wells, in his Curious and Interesting Numbers of $1986$, the term repunit was coined by Albert H. Beiler.

Linguistic Note

The derivation of the term repunit is clear: it comes from repeated unit.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $11$
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1,111,111,111,111,111,111$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): Glossary
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $11$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1,111,111,111,111,111,111$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): repunit
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): repunit