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August 9th, 2017, 11:12 PM   #1
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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 $n=2$ ; $M_2 = (X^n-(X-1)^n) = 2x-1$:

\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.

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August 10th, 2017, 06:27 AM   #2
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Here how the clock works for n=2:



and for n=3

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August 11th, 2017, 12:12 AM   #3
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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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