[seqfan] Interesting Recreational Sequence

[Jack Brennen]

> Will this sequence eventually become "all zeros" or can it be shown
> that non-zero entries exist ad infinitum?

I believe you can show that any integer whose representation does
not contain a '1' digit, and which ends in '3', '7', or '9', has
a multiple consisting of just the digit '1' repeated some number
of times.  This is sufficient to prove an infinite number of
non-zero entries, since there are an infinite number of integers
which contain every digit but '1', and which end in '3', '7', or '9'.
For instance:

  203456789 divides evenly into (10^101710278-1)/9.