Hello VQC! Nice to see you.
The n0 base and triangle staircase numbers are derived from f, so they scale with every c value, correct?
On another thought: For the grid shortcut, does our program/algorithm need to be able to generate the elements surrounding the na transform in e,1 and -f,1?? The na transform lands us right in between (an) and (bn) in e,1 and a(n-1) and b(n-1) in -f,1. The movement from the na transform to the correct (an) and (bn) t or x values is very similar to the formula you described in your IP hopping post >>8040. The movement to (an) and (bn) is definitely two adjacent staircase numbers, and for a(n-1) and b(n-1) it happens as well. For c145 those numbers are 2 and 3 in e,1.
>To find the staircase numbers for an odd value, we add one to the value then divide it by two. Then the number is equal to the result added to the result minus one. Calculating this for the number we started with, would make two familiar values. Adding two side by side (t aligned) x values in e,1 and -f,1 would also make a staircase number.
>When na is odd, what do you do to find an identifier for the element where the x is equal to one of the staircase numbers for na? And if na is even, for n-1?