I wrote:

> I think superparticulars are the smallest unison vectors for a given taxicab
distance in the
triangular
> lattice, if the lattice is constructed Kees' way.

This seems to be true until you run out of superparticulars for the given prime
limit. This happens
at 81:80 for the 5-prime-limit. The first smaller unison vector obtained by
searching slightly larger
regions of the lattice is 2025:2048. 2048 - 2025 = 23, so it's not too
surprising that the numbers
in this ratio are on the order of 23 times the numbers in 80:81.

In the 7-prime-limit, this happens at 4374:4375. The first smaller unison vector
obtained by
searching slightly larger regions of the lattice is 250000:250047. 250047 -
250000 = 47, so it's
not too surprising that the numbers in this ratio are on the order of 47 times
the numbers in
4374:4375. Make sense?