>>5887

>The final steps involve finding a base using (f-1)/8 for each of the eight triangles (some a bit bigger than others by a unit in length) which is larger than (n-1)/8 BUT smaller than (x+n)/8.

Pics attached are an idea of how this could look for the c6701 and c27707 examples.

Starting with the (n-1)+(f-1) portion in the middle, a new red square outline has been added (f-1)/8 units from the center.

For the c27707, the light green squares around that red outline represent the u1=(f-1)/8 + 1 value of 23. And the light green squares represent the u2=(f-1)/8 value of 22.

The c6107 example computes to u1=17 and u2=16.

Attached are also rough calculations showing successful matches in 7 steps.

>>5950

Some additional examples for (x+n)=83 for different f mod 8 and n starting values.

Looks like the earlier formula for f can be generalized for e movements within the same x+n.

e = e + 2n

f = f - 2(n-1)

So there's our (n-1) again.

Also looks like there might be some relationship between f mod 8 and (n-1)+(f-1) mod 8, but not certain of that yet.

>>5959

>make an equation for finding the range of n and (x+n) for a given c if that would help (it sounds like it would to me but I don't tend to get feedback about these things)

I also looked for the formula for max n in a given x+n. But ran into a problem where that max n could be greater than the n we were searching for during iteration, so tabled the idea.

The starting n and increments are known - I've posted that code snippet previously. It would be nice to know that max n value. If not for iteration purposes, then perhaps for another use down the road.

>>5942

Pics attached are visuals for the e = e + 2n movement that VQC referenced previously.

Starting from a new test record for c86747, these images show the e movement and affects on f moving 2 records to the right as well as 2 records left.

For reference, the starting prime solution is:

(311,12,36) = {311:12:294:71:223:389} = 86747; f=278; (x+n)=83; u=41; (d+n)=306

One image shows the regular formula for nn + 2d(n-1) + f - 1 with the (f-1) portion in the center.

The other image breaks the 2d(n-1) into another (n-1) piece and combines with (f-1).

All images are partial views of the x+n=83 square.

>>5976

>>5985

Topol, thanks for stitching these together.

>>5977

I think the most compelling of the two views is the (n-1)+(f-1) example, which shows a single green square moving around the top portion.

These gifs show only 5 iterations, but many more examples for the same x+n=83 can be found by decreasing n from 12 to 2.

I believe the following repeating patterns apply to (n-1)+(f-1) mod 8, but would appreciate someone else verifying:

f mod 8 = 0

Starting from n=2

(n-1)+(f-1) mod 8 pattern: 0, 2, 4, 6

f mod 8 = 1

Starting from n=3

(n-1)+(f-1) mod 8 pattern: 2, 4, 6, 0

f mod 8 = 2

Starting from n=2

(n-1)+(f-1) mod 8 pattern: 2, 4, 6, 0

f mod 8 = 4

Starting from n=2

(n-1)+(f-1) mod 8 pattern: 4, 6, 0, 2

f mod 8 = 5

Starting from n=3

(n-1)+(f-1) mod 8 pattern: 6, 4, 2, 0

f mod 8 = 6

Starting from n=2

(n-1)+(f-1) mod 8 pattern: 6, 0, 2, 4

These mod patterns apply only within the same f mod 8 value. Keep in mind that the e = e + 2n movement changes the f mod 8 value for each record.

So for the c86747 record, 2 left and 2 right posted, the (n-1)+(f-1) mod 8 values are 4, 6, 0, 2, 4.

>>5996

Congratulations, GA. Tremendous accomplishment.

>>5991

Still playing with the odd x+n square and triangles, but managed to take things a bit further.

Pics attached show a bit of a progression:

1) Initial layout of 8 triangles around a center square.

2) Iterating the 8 triangles sequentially and filling in numerical values.

3) Dynamically generating the n, d, f view for c=6107. (This corresponds to the nn + 2d(n-1) + f - 1 layout from >>5976.)

>>6003

One more example for c86747. The prime record posted in >>5985.

Interesting that the nn portion is now distributed to the corners.

Now able to generate odd x+n squares dynamically to image format.

Attached are animated examples again for x+n=83 where n=11 or 12 in the same two styles mentioned previously at >>5976.

These records are not associated by e=e+2n movement. Currently just testing for any layout adjustments.