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August 9th, 2017, 11:12 PM  #1 
Senior Member Joined: Dec 2012 Posts: 1,015 Thanks: 24  Complicate number calculator
I'm writing a simple VB6 software to play with my Complicate Numbers. Here a screenshot: It show how an integer $P$ can be written in term of a Complicate Number, that is build as an Integer Pure Power, plus a rest. Here and example for $n=2$ ; $M_2 = (X^n(X1)^n) = 2x1$: \begin{table} [htbp] x Int.Root Rest Complicate Number 1 1 0 = 1^2+0 = 1 M_2+0 2 1 1 = 1^2+1 = 1 M_2+1 3 1 2 = 1^2+2 = 1 M_2+2 4 2 0 = 2^2+0 = 2 M_2+0 5 2 1 = 2^2+1 = 2 M_2+1 6 2 2 = 2^2+2 = 2 M_2+2 7 2 3 = 2^2+3 = 2 M_2+3 8 2 4 = 2^2+4 = 2 M_2+4 9 3 0 = 3^2+0 = 3 M_2+0 10 3 1 = 3^2+1 = 3 M_2+1 11 3 2 = 3^2+2 = 3 M_2+2 12 3 3 = 3^2+3 = 3 M_2+3 13 3 4 = 3^2+4 = 3 M_2+4 \end{table} You can insert 2 numbers, choose the Base (the exponent $n$) than it show the two numbers on the Two Hand Clock, and their Sum. 
August 10th, 2017, 06:27 AM  #2 
Senior Member Joined: Dec 2012 Posts: 1,015 Thanks: 24 
Here how the clock works for n=2: and for n=3 
August 11th, 2017, 12:12 AM  #3 
Senior Member Joined: Dec 2012 Posts: 1,015 Thanks: 24 
Here the .Gif film where you can see both $n=2$ and $n=3$ counter: Some interesting behaviour are immediately visible:  the hours hand in case $n=2$ moves forward, while the $n=3$ after reach $2$ moves backward.  the Sum of 2 equal numbers, one in base $2$ the other in base $3$ produce a nice behaviour on the Rest ...etc... Last edited by complicatemodulus; August 11th, 2017 at 12:18 AM. 

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