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for question related to conjectures.
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Why is $\sup f_- (n) \inf f_+ (m) = \frac{5}{4} $?
So the numbers from the OP can ( more or less) be given by these infinite series and hence the whole conjectures can be stated by these infinite series. … But many related conjectures exist.
Many might turn out to be equivalent or have already been shown to be equivalent. …