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Has this form of the shortcut Collatz conjecture been studied?

by rpz on 8/18/23, 3:27 AM with 1 comments

• by rpz on 8/18/23, 3:27 AM

  I was messing around looking into the collatz conjecture in q/k4 and I realized that I could write the short cut collatz function without any conditionals as follows by taking advantage of the fact that you can use the result of x mod 2 to zero out some terms when x is even.

  note: no operator precedence in q/k

    q)cc:{(x+(2*x*m)+m:x mod 2)div 2}
    q)cc til 20
   0 2 1 5 2 8 3 11 4 14 5 17 6 20 7 23 8 26 9 29
  

  After some algebra I arrived at

    cc:{(x*1+x)-(x div 2)*1+2*x}
  

  Figured I'd share what I found since I don't see this formula mentioned on https://en.wikipedia.org/wiki/Collatz_conjecture . Has anybody else encountered this formula?

  I've linked a chart of the function with its definition in more familiar mathematical notation. It's extended onto the reals by utilizing the floor function.

  PS: Notation is a tool of thought!