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July 2nd, 2015, 04:32 AM   #1
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The multi-ordered numbers

The leading numbers and the reversed numbers are just 2 particular cases of the multi-ordered numbers.
The multi-ordered numbers are noted M index i (s,r) where i is the permutation order s the size of the sequence generated and r the rank of the number. See the details on the threads "Leading numbers" and "the reversed numbers".
As an example I will give the values of M(3,1)
There are 24 values (4!)
The first 4 columns indicate the divisibility order and the fifth the value of M(4,1).
The lines indicate the index i varying from 1 to 24


2 3 5 7 158 (the leading numbers)
2 3 7 5 152
2 5 3 7 4
2 5 7 3 54
2 7 3 5 202
2 7 5 3 48
3 2 5 7 123
3 2 7 5 117
3 5 2 7 144
3 5 7 2 159
3 7 2 5 132
3 7 5 2 153
5 2 3 7 25
5 2 7 3 75
5 3 2 7 200
5 3 7 2 5
5 7 2 3 90
5 7 3 2 55
7 2 3 5 7
7 2 5 3 63
7 3 2 5 182
7 3 5 2 203
7 5 2 3 84
7 5 3 2 49 (the reversed numbers)


So for s=n we will have n! values corresponding to all the permutations

M(10,1) for examples will have 3628800 values (10!)

Where are going to lead us all those numbers?

Not easy to compute them in fact but maybe there is something more interesting to come.
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