The 82000 sequence is still generating interest.
The sequence has also made it into the Online Encyclopaedia of Integer Sequences, as A258107!
I have also found an early mention of the special properties of 82000, in this exchange on a French puzzle forum, from October 2008. In the thread, user “dhrm77” challenges others to identify “a number greater than 1, which is written only with 0 and 1 in bases 2, 3, 4 and 5.” More excitingly, he claims that “this number is unique”, which made me hopeful that there might be a proof of this fact further down the thread. No such luck though, as “dhrm77” later admits (in post #11) that he has no proof of uniqueness, and discusses the way in which the chance of finding a solution becomes increasingly small as the size of the numbers you are checking increases.
The final comment (#13) refers users to OEIS sequence A146025, which “dhrm77” (presumably the “Daniel Mondot” cited as the sequence author) has apparently submitted and had accepted in the OEIS. Whether “dhrm77” discovered the interesting property of 82000 himself, or whether he got it from some earlier source is not clear.