[seqfan] Interesting Recreational Sequence
Jack Brennen
jack at brennen.net
Mon Jan 19 17:27:49 CET 2004
> 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.
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