Spiral Permutation Sequence
Japt, 20 19 16 bytes
V=U¬c)²-V *2-U+2

Test it online!
Based on the observation that

 F(N) = ceil(N^.5) * (ceil(N^.5)-1) - N + 2

Or, rather, that

 F(N) = the first square greater than or equal to N, minus its square root, minus N, plus 2.

I don't know if this explanation is on the OEIS page, as I haven't looked at it yet.