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单词 PandigitalNumber
释义

pandigital number


Given a base b integer

n=i=1kdibi-1

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

bb-1+d=2b-1db(b-1)-d,

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

d=1b-1dbd.

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.

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更新时间:2025/5/4 7:06:28