I have tried to translate the Mathematica-Code of OEIS (A219954):

with MmaTranslator. In the translator occurs an error message with the IF-Statement ...

I will be happy to have this in Maple. I am interested in the digitCount in the above Code.

Sequence is:

I have written a maple-code that is visualizing cycles or periods of inverse numbers in any base in a coloured plot.

For example 1/13=0,76923 076923 ... (so period-lenght is 6, the cycle-digits are visualized)

Now I would like to run the Maple Code wich produces the plot (via display-comand) on an ipad.

The ipad will be located in a museum or galerie. In the most easily way the user just touch a button on the ipad-screen and the maple-code produces a random plot which is displayed. Later some choosable parameters for the plot are added.

I have make some tests with embedded components in Maple.

So my idea is to do this with maple-player. I read about Maple Player features:

- Interact with applications that make use of embedded components, such as sliders, buttons, and math entry boxes. Maple will perform the computations and display updated results and visualizations

Questions:

1) how do I run Maple code in Maple Player (a little example with a button- and a plot-component will help)

2) do I need to upgrade Maple 2021  to do that ?

3) What does a mapleplayer license cost for each ipad ?

Thanks for support :)

For example: n=78 (is squarefree because 2 x 3 x 13)

Possible periodlenghts in different bases for 1/78  are  {2,3,4,6,12} this is calculated with Multiplicative-Order (Maple).

Now we pick a period from above, for example 6.

The question is:

Which possible bases exist for 1/78 with  periodlenght of 6 ?

The result is: possible bases calculated with Multiplicative-Order
are {17,23,29,35,43,49}.

Question:
Is there a formular to calculate the bases directly or with less calculations than the Maple-Command ?

Thanks for helping :)

# this is an example:

with(plots);

A := [[[6, 13], [6, 7], [5, 7], [5, 5], [7, 5], [7, 4], [4, 4], [4, 13]], [[13, 13], [13, 20], [20, 20], [20, 23], [22, 23], [22, 22], [23, 22], [23, 16], [16, 16], [16, 9], [9, 9], [9, 6], [7, 6], [7, 7], [6, 7], [6, 13]], [[13, 23], [20, 23], [20, 20], [13, 20]], [[13, 24], [20, 24], [20, 23], [13, 23]], [[22, 24], [22, 23], [20, 23], [20, 24]], [[24, 24], [24, 22], [23, 22], [23, 23], [22, 23], [22, 24]], [[22, 22], [22, 23], [23, 23], [23, 22]], [[22, 25], [25, 25], [25, 16], [23, 16], [23, 22], [24, 22], [24, 24], [22, 24]], [[25, 6], [16, 6], [16, 9], [23, 9], [23, 16], [25, 16]], [[9, 6], [9, 9], [16, 9], [16, 6]], [[6, 6], [6, 7], [7, 7], [7, 6]], [[6, 20], [13, 20], [13, 13], [6, 13]], [[20, 28], [28, 28], [28, 16], [25, 16], [25, 25], [22, 25], [22, 24], [20, 24]], [[16, 5], [9, 5], [9, 6], [16, 6]], [[7, 5], [7, 6], [9, 6], [9, 5]], [[5, 5], [5, 7], [6, 7], [6, 6], [7, 6], [7, 5]], [[4, 23], [13, 23], [13, 20], [6, 20], [6, 13], [4, 13]], [[23, 9], [16, 9], [16, 16], [23, 16]], [[9, 1], [1, 1], [1, 13], [4, 13], [4, 4], [7, 4], [7, 5], [9, 5]]];
NULL;

arte := seq(polygonplot([A[i]], color = ColorTools:-Color([rand()/10^12, rand()/10^12, rand()/10^12]), axes = none, style = polygon, view = [1 .. max(A[]), 1 .. max(A[][])]), i = 1 .. nops(A));
display(arte);

I have created some plots of inverse primes  like this example1.pdf .

The filled color-shape in the middle is what I want do do with all areas in this picture or in other pictures.

In other words the goal is to fill the differnt areas in the print with different colors.

So I need to find the points of the Polygons, as I have done by hand with that yellow Polygon.

A procdure that is ready will give give the crosspoints of the lines.

These are the line-coordinates (the 1st number ist the number of iterations)

2*L[1]=number of lines in L

L:=[14, [[1, 1], [1, 26]], [[1, 26], [26, 26]], [[26, 26], [26, 37]], [[26, 37], [37, 37]], [[37, 37], [37, 39]], [[37, 39], [39, 39]], [[39, 39], [39, 20]], [[39, 20], [20, 20]], [[20, 20], [20, 23]], [[20, 23], [23, 23]], [[23, 23], [23, 30]], [[23, 30], [30, 30]], [[30, 30], [30, 70]], [[30, 70], [70, 70]], [[70, 70], [70, 45]], [[70, 45], [45, 45]], [[45, 45], [45, 34]], [[45, 34], [34, 34]], [[34, 34], [34, 32]], [[34, 32], [32, 32]], [[32, 32], [32, 51]], [[32, 51], [51, 51]], [[51, 51], [51, 48]], [[51, 48], [48, 48]], [[48, 48], [48, 41]], [[48, 41], [41, 41]], [[41, 41], [41, 1]], [[41, 1], [1, 1]]]

These are the crosspoints:

cp := [[23, 26], [30, 37], [32, 37], [26, 30], [48, 45], [39, 34], [41, 34], [45, 41]]

To plot the pdf I used this code:

poly2 := [[32, 32], [34, 32], [34, 34], [39, 34], [39, 39], [37, 39], [37, 37], [32, 37]]

poly 2 is just an axample, how it looks like when its ready.

display(seq(line(op(L[i])), i = 2 .. 2*L[1] + 1), polygonplot([poly2], color = "Resene GoldenTainoi", axes = none, style = polygon), color = blue, thickness = 0.8);

So I hope, you can help me :)

This is a beautyfull way to paint a prime  by just printing the remainders of the recursive dividing of the inverse prime in lines.

Thanks a lot,

Arno