Why does Intel produce core i3, core i5 and core i7 processors; but not core i2, core i4 or core i6 processors?
I don't have any particular source, but I'd imagine this is simply due to marketing reasons more than anything technical. As wikipedia states:
" Intel introduced a new naming scheme for its Core processors. There are three variants, Core i3, Core i5 and Core i7, but the names no longer correspond to specific technical features like the number of cores. Instead, the brand is now divided from low-level (i3), through mid-range (i5) to high-end performance (i7)"

And thus I'd assume the absence of 2, 4, and 6 is probably just as a way to further prevent confusion from Intels previous naming scheme of Core 2 Duo and Quad Core processors, where the name originally symbolized the number of cores.