Why? If all I want is a mapping from i to my index space, I don't see why we should have to shift i down one first. Note that we don't have to come up with the same mapping that the zero-based indexing would.

Because then you'd get to the next row before you've finished N elements.

Yeah, I don't see what you're getting at. Where does "before" come in? We're assuming an arbitrary positive integer, not a sequence. And even if it was a sequence, I see no problems. Let's assume N == 5, then the mappings we get are:

   1 -> 2
   2 -> 3
   3 -> 4
   4 -> 5
   5 -> 1
   6 -> 2
   7 -> 3
   8 -> 4
   9 -> 5
  10 -> 1
  ...

This is a valid mapping from Z+ to our index space. Is your objection that 2 does not map to 2, 3 does not map to 3? That may be a useful property, but (i % N) + 1 is still a valid mapping without that property.