## You are here

Homepandigital number

## Primary tabs

# pandigital number

$n=\sum_{{i=1}}^{k}d_{i}b^{{i-1}}$ |

where $d_{1}$ is the least significant digit and $d_{k}$ is the most significant, and $k\geq b$, if for each $-1<m<b$ there is at least one $d_{x}=m$ among the digits of $n$, then $n$ is a pandigital number in base $b$.

The smallest pandigital number in base $b$ is

$b^{{b-1}}+\sum_{{d=2}}^{{b-1}}db^{{(b-1)-d}},$ |

while the largest (with only one instance of each digit) is

$\sum_{{d=1}}^{{b-1}}db^{d}.$ |

There are infinitely many pandigital numbers with more than one instance of one or more digits.

If $b$ is not prime, a pandigital number must have at least $b+1$ digits to be prime. With $k=b$ for the length of digits of a pandigital number $n$, it follows from the divisibility rules in that base that $(b-1)|n$.

Sometimes a number with at least one instance each of the digits 1 through $b-1$ but no instances of 0 is called a zeroless pandigital number.

## Mathematics Subject Classification

11A63*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections