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Transform procedure that changes one prime quadratic chain into another

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  • aldrich617
    I have taken my transform idea that was posted on 5/22 and put it into a programming procedure. The exact mechanism by which it works is a bit of a puzzle.
    Message 1 of 1 , May 28, 2008
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      I have taken my transform idea that was posted on 5/22
      and put it into a programming procedure. The exact mechanism
      by which it works is a bit of a puzzle. Somehow it takes
      prime factors that were in the old sequence(not necessarily
      in the chain itself} scrambles them, and makes them
      reappear with scaffolding factors left over from the
      transform construction phase that must be removed
      to see the entire chain. sometimes it is possible to create
      an array with over a hundred elements by using different
      scaffolding numbers in several consecutive transforms.

      Procedure transform:

      a1,a2,a3 ; the first three elements of the old prime
      chain in 36x^2 - 810x + 2573
      (2753, 1979, 1277)

      inc := (a3 -a2) - (a2 - a1); The constant increment of
      the quadratic is calculated

      C := 2; the root chosen as the scaffolding factor

      d := {c*c*a2 - c*c*a1)/c; the interval in which new terms
      are to be inserted.

      e := c div 2;
      if odd(c) then F1 := D - inc*e;
      if odd (c + 1) then F1 := D -(inc*e - inc/2);
      f2 := f1 + inc;
      the proper size and location of the quadratic
      variable increment is calculated

      a1 := c*c*a1;
      a2 := a1 + f1;
      a3 := a2 + f2; the first three elements of the new prime
      chain are figured before scaffolding factors
      are removed. (11012, 9428, 7916)

      The old chain had 44 elements.
      the new chain has 46 elements

      Aldrich Stevens
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