Why isn't 0 in A034710?

[Max Alekseyev]

On 9/21/07, Jonathan Post <jvospost3 at gmail.com> wrote:

> Why isn't 0 in A034710  Numbers for which the sum of digits equals the
> product of digits?

I think this sequence assume positive integers.

> That is, why not correct A034710 to 0, 1, 2, 3, 4,
> 5, 6, 7, 8, 9, 22, 123, 132, 213, 231, 312, 321, 1124, ...
> with offset 0,3?

Why the offset is 0? Even having 0 in the sequence shouldn't change
the offset to 0. As many other sequences representing certain subsets
of the integers, it should have the offset 1.

> 0 would also thus be in A061672 Smallest number formed by a set
> of digits whose product = sum of the digits?

A061672 also contains positive integers.

Zero is a very special number, its leading digit is 0 that is not
allowed for other numbers. If we try to fit the number zero into this
rule, it should contain no digits at all (the "empty" number) with the
sum of digits equal 0 and the product of digits equal 1.
But I would better vote for excluding zero from the aforementioned
sequences, as it is now.

Regards,
Max