>What do these look like?
Pic attached shows some ideas of how the n,d, and f values may grow within the same odd x+n.
Example is for f mod 8 = 0 and x+n=13. I have attempted to retain as much symmetry as possible and moved the nn-1 portion to the edges.
The point here is to try and understand how n grows in relation to a constant f value. The green arrows indicate possible paths. And constant n with growth in f values are indicated by blue arrows.