Polydivisible Number/Examples/381,654,729/Mistake

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Source Work

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary
$381,654,729$


Mistake

The unique integer such that the number formed by the first $n$ digits is divisible by the digit $n$.


That should read:

The unique pandigital integer (in the sense that zero is excluded) such that the number formed by the first $n$ digits is divisible by the digit $n$.


It is a trivial task to create a $9$-digit integer with this property that is not pandigital. Straight off the top of my head:

$222 \, 456 \, 564$


It is also worth pointing out that $3 \, 816 \, 547 \, 290$ is also pandigital (but in the sense that zero is included) and also has the same property -- although $10$ is not a digit as such.

Numbers with this property are referred to as polydivisible.


Sources