Alternation Numbers
 

Define an "alternation number" as an integer whose (decimal)
representation contains exactly two different digit values,
appearing in alternating place values (e.g. 1212 and 37373).

Find an alternation number which factors into two (or more)
alternation numbers each containing at least three digits
(if possible).

There's no solutions of the form: aba * cdc.

what about the forms: aba * aca , aba * cac , aba * bcb , aba * cbc ?

None of them work.

[SPOILER]Tested all alternation numbers as far as 98,989,898,989,898,989
= 9*10^16 + 8*10^15 + ... + 9*10^0
None of the factorizations work.
[/SPOILER]

Oops. I have misread the puzzle.
My trivial effort above looked only at the [I]prime factorizations[/I] of alternation numbers, but the problem does not state that the alternation factors have to be prime.
Sorry. Keep trying.