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May 19, 2016 at 17:39 comment added Kevin O'Bryant Either the set is a $B^*[999] $ set, or there is a positive integer with at least 1000 representations.
May 16, 2016 at 19:20 comment added Shahrooz Thanks for your answer. Also, I saw your paper and it is interesting. I hope you can update it asap. As I understood, this problem is open, yes? Also, the question asks about the existence of a special integer which can be written in thousand different ways. But in your definition, the sequence has this property that each integer can be written in at most $g$ ways (allowing repetition).
May 16, 2016 at 7:38 vote accept rationalbeing
May 16, 2016 at 2:12 history answered Kevin O'Bryant CC BY-SA 3.0