# Are there known natural problems of intermediate degrees of unsolvability?

I know there exist intermediate degrees of unsolvability, i.e. there are undecidable problems which can be reduced to the Halting Problem, but not vice versa. Are there any "natural" problems known or suspected to fall into this category?

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Is the number of $N$-state two-symbol Turing machines (up to renumbering of states) that halt on the empty input, odd?