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- All the things we can calculate/find/whatever with our given c:
- >d, e and f (d and e being the variables necessary for calculation, “the collapse of the superposition”)
- >the cell where (a, b) = (1, c)
- >the cell in (e, 1) with our e and n=1
- >the cell in (-f, n-1) with our f and n=n-1 (0)
- >the (e, 1) and (-f, n-1) cells related to our (1, c) cell’s e and f values
- >if positive f is a square and increasing d by 1 and e by 2 results in the same positive f value, we can calculate all of endxab
- >the place in column 0 (e, 0) at which our c^2 is (which may be in more than just (0, 0), in which case I’m not completely sure this is calculable without ironically having to factorize)
- All the things we can find if we know a and b:
- >(e, n)
- >the cell in (-f, n) with our f and the actual n from our c
- >big_n, which is n at the cell where (1, a) or (1, b) = (1, c) (i.e. every prime number can only be calculated with 1 and itself as the a and b values, and so they’ll only ever have one n value)
- >the (e, 1) and (-f, n-1) cells related to our (1, a) and (1, b) cells’ e and f values
- >the cells in (e, 1) at which na and nb are n cells apart (n being the correct n for our c)
- >t
- >with the cells in n=1 that we can find related to our c (and all others), the cell at n+=2 has the same n and x values but a, b and d have increased by 1
- >for our given c’s (e, n), there will be values in a cell at (e+2n,n) (which is meant to be an important pattern too)
- >the cell at which a = a^2 and b = b^2, the increasing powers, and the other binomial-related combinations of a and b
- >the x value at (e,n) is equal to the x value where d[t] = na+x
- >a pattern of (n-1) as a factor of each d[t] value at (e,1) which is different (increasingly) from the pattern of factors of n in a[t] which gives us the offset that is used to solve the problem and thus get the cell at (e,1) to do all the work for you
- All the things we can find that have been suggested to be important but not looked into in very much detail as far as I can tell:
- >negative values of x for cell (1, 1) and then cells 2 to the right
- >how many times numbers that are the product of three, four, five etc prime numbers turn up for a given e (it’s not linear, apparently)
- >All products (integers) c that are the sum of two squares appear (only) in columns where e=0,1,4,9,16,25,..
- >The value of x at (e,1) for na (a[t]) is the value of x at (e,n) (I only put this in the last section because I don’t completely understand the na (a[t]) part)
- >think about the distribution of n and (n-1) in cell (e,1) in the a[t] and d[t] values respectively. This is the quick way to utilising f.
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