Let be an infinite sequence of positive integers, such that, if we define to be the number of indices such that , then we have for every infinitely many such that , where . In my previous post I claimed that such sequences exist, and in due time I will prove this claim, but for now, let’s assume it.

Now, let be small and be the sequence of all such that . Then I’d like to bluntly conjecture that there exist infinitely many such that , for some absolute . In particular, goes to as goes to , that is:

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