@Vepir so in the last edition of the problem, we allow one-element subsequences, but the catch is that we insist on uniqueness of the representation, and the answer by Hagen von Eitzen is that there are no such nice sequences. And, also, we need to represent every positive integer, not only those in $\mathcal D$. (And I am so confused at this point, so I need to read it all over, to see what the question asks, and whether it was indeed answered, and which sequence is an example of what.)
@Vepir If only integers in $\mathcal{D}$ need to be represented (which I had overlooked) then indeed one should NOT allow one element subsequences (if the problem is to be non-trivial). The sequence $1,2,4,8,16,...,2^{n-1},...$ is interesting in that it could represent every integer, and in particular its own elements, $2^{n-1}=-2^{n-1}+2^n$ (whether or not you allow one element sequences.) $3=-1+4, 5=1-4+8, 6=-2+8, 7=-1+8, 9=16-7$ and plug in the representation for $7$ and distribute the $-$ sign, $9=16-(-1+8)=1-8+16$, etc.
@Vepir I don't think that a comment from miracle173 implies that every sequence is nice. Finger pointing (on my part, to a particular sequence) is certainly not nice at all, but you cannot get an odd number starting with the sequence of even numbers.
@XanderHenderson Yes, I kind of did move on, almost, I see you put a critical comment on an answer (by user @user) neighboring the answer that I was complaining about yesterday, but you did not leave any comment on the answer that I was complaining about (by user @Henry). I am not suggesting that I know what you should or should not have done, I just wanted to make sure it was not some kind of a technical mistake or misunderstanding regarding which answer exactly I had suggested was inadequate.
@XanderHenderson Thanks, I guess I just couldn't let it go without making some fuss about it first. It didn't help that my first comment to that answer was addressed but I believe inadequately, by the answerer (perhaps some misunderstanding, but I think my comment was clear, and the answerer has plenty rep, so I expected they would easily understand my criticism). Thank you for reminding about the word "politely", I hope I have not crossed some boundaries that I shouldn't ...
@XanderHenderson I already did (2) and multiple (4). I do not see a "low quality" or "wrong answer" flag. I do have 10K but do not see a button for "vote to delete an answer" (that last thing addressed to @Jack).
and here is the answer that I find wrong math.stackexchange.com/q/3448311 now, as a new user of this chat room, what is the difference between the "send" and the "upload" button?
