Sorry, I misread this. I read your question as O outputting some function T that is most likely to answer some set of questions you want to know the answer to (which would be self-referential as these questions depend on the output of T). I think I understand your question now.
What kind of ability do you have to know the "true value" of your sequence B?
If the paperclip maximizer P is able to control the value of your turing machine, and if you are a one-boxing AI (and this is known to P) then of course you can make deals/communicate with P. In ... (read more)
Looks like you're making a logical error. Creating a machine that solves the halting problem is prohibited by logic. For many applications assuming a sufficiently powerful and logically consistent oracle is good enough but precisely these kinds of games you are playing, where you ask a machine to predict its own output/the output of a system involving itself, are where you get logically inconsistent. Indeed, imagine asking the oracle to simulate an equivalent version of itself and to output the the opposite answer to what its simulation outputs. This may s... (read more)