Distance Table

From OPU Wiki

Hope someone can figure this out..

I pulled this table from Outpost (by trial-and-error method):

1	5	13	25	41	61	85	...
5	9	17	29	45	65	89	...
13	17	25	37	53	73	97	...
25	29	37	49	61	85	109	...
41	45	53	65	77	101	125	...
...	...	...	...	...	...	...	...

it shows the distance from the "origin" sqaure (topleft, the one named 1). These values are returned by the ClosestEnumerator and used as a param in the InRangeEnumerator (see Enumerators.h). There has to be a mathematicle function between them, but i didn't spend much time on it yet. NOTE: the numbers above are decimal (NOT hex!)

TH300:

assuming there are a few mistakes in it... the numbers on the diagonal line starting at 1 are the square numbers of every second integer starting with 1: (for some stupid reason <math> doesn't work)

1² = 1

3² = 9

5² = 25

7² = 49

9² = 81 //thats were you figured out 77 which might be wrong -- Eddy: you prolly right: if you check the number to the topright of those, it's ALWAYS +4, so it must be 81 then

all others numbers can be determined by adding up the two numbers on said diogonal which are in the same column/row and right-shifting the result by 1.

The formula for all values:

value = ((2x - 1)² + (2y - 1)²) / 2

(for number 1 x and y are 1)

Eddy

Seems like you figured it out.. great work!

op2hacker

Looks a lot like Pascal's triangle to me. (In essence it is a triangle, and makes more sense written as such). Thus it's just a special type of geometric sequence.