pandigital number

Given a base b integer


where d1 is the least significant digit and dk is the most significant, and kb, if for each -1<m<b there is at least one dx=m among the digits of n, then n is a pandigital number in base b.

The smallest pandigital number in base b is


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


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 rulesMathworldPlanetmath 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.

Title pandigital number
Canonical name PandigitalNumber
Date of creation 2013-03-22 16:04:28
Last modified on 2013-03-22 16:04:28
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 4
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A63
Defines zeroless pandigital number