The first few pandigital base 10 numbers are given by (sequence A171102 in the OEIS): The smallest pandigital number in a given base b is an integer of the form The following table lists the smallest pandigital numbers of a few selected bases.
In a trivial sense, all positive integers are pandigital in unary (or tallying).
The larger the base, the rarer pandigital numbers become, though one can always find runs of
Conversely, the smaller the base, the fewer pandigital numbers without redundant digits there are.
Sometimes, the term is used to refer only to pandigital numbers with no redundant digits.
In some cases, a number might be called pandigital even if it doesn't have a zero as a significant digit, for example, 923456781 (these are sometimes referred to as "zeroless pandigital numbers").
The sum of the digits 0 to 9 is 45, passing the divisibility rule for both 3 and 9.
The first base 10 pandigital prime is 10123457689; OEIS: A050288 lists more.
The smallest pandigital palindromic number in base 10 is 1023456789876543201.
A pandigital Friedman number without redundant digits is the square: 2170348569 = 465872 + (0 × 139).
The concept of a "pandigital approximation" was introduced by Erich Friedman in 2004.
[2] While much of what has been said does not apply to Roman numerals, there are pandigital numbers: MCDXLIV, MCDXLVI, MCDLXIV, MCDLXVI, MDCXLIV, MDCXLVI, MDCLXIV, MDCLXVI.
Some credit card companies use pandigital numbers with redundant digits as fictitious credit card numbers (while others use strings of zeroes).