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Jun 21st, 2018
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  1. All the things we can calculate/find/whatever with our given c:
  2. >d, e and f (d and e being the variables necessary for calculation, “the collapse of the superposition”)
  3. >the cell where (a, b) = (1, c)
  4. >the cell in (e, 1) with our e and n=1
  5. >the cell in (-f, n-1) with our f and n=n-1 (0)
  6. >the (e, 1) and (-f, n-1) cells related to our (1, c) cell’s e and f values
  7. >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
  8. >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)
  9.  
  10. All the things we can find if we know a and b:
  11. >(e, n)
  12. >the cell in (-f, n) with our f and the actual n from our c
  13. >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)
  14. >the (e, 1) and (-f, n-1) cells related to our (1, a) and (1, b) cells’ e and f values
  15. >the cells in (e, 1) at which na and nb are n cells apart (n being the correct n for our c)
  16. >t
  17. >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
  18. >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)
  19. >the cell at which a = a^2 and b = b^2, the increasing powers, and the other binomial-related combinations of a and b
  20. >the x value at (e,n) is equal to the x value where d[t] = na+x
  21. >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
  22.  
  23. 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:
  24. >negative values of x for cell (1, 1) and then cells 2 to the right
  25. >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)
  26. >All products (integers) c that are the sum of two squares appear (only) in columns where e=0,1,4,9,16,25,..
  27. >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)
  28. >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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