nine reduction question

[lamaken]

Hello,
My Name Is Àlex, from StcU
I have been thinking a lot with the follow

of number 9 casuística
https://alkasoft.org/nine/

I have build an small script to do the next operations:

from a given number
like 14
we multiply 9 so 126
"Here the trick: 126 is mulitple by 9 so we could remove the last number(6) so be knew the addition from the all the digits has to ber mutiple with 9"

so the next is 12
"we are decreasing"

we multiply 9 so 108
we remove 8 so is obius (1+0+?=9)
.. and go ..

10 * 9 = 90 < (0,3)
9 * 9 = 81
8 * 9 = 72
7 * 9 = 63
6 * 9 = 54
5 * 9 = 45
4 * 9 = 36
3 * 9 = 27
2 * 9 = 18
1 * 9 = 9 < (9,12)

only when the last digit is (0 or 9) we have to mark to know it.

so the result is

[0,3] [9,12]

[9,12]: iteration 12 is 9
[0/3]: iteration 3 is 0


Decode output
9 / 9 = 1
18 / 9 = 2
27 / 9 = 3
36 / 9 = 4
45 / 9 = 5
54 / 9 = 6
63 / 9 = 7
72 / 9 = 8
81 / 9 = 9 < (0)
90 / 9 = 10
108 / 9 = 12
126 / 9 = 14
14

Only know whether this could be useful for anything.

SOrry for inconviniences

 

[HallsofIvy]

I don't understand your notation. In "90< (0, 3)" and "9< (9, 12)" what do "(0, 3)" and *(9, 12)" mean?

 

[lamaken]

Hello

Sorry, the notation is a reference to me to keep the number 0 in the third(3) iteration
or 9 on 12th

we want to encode the following
14

Encode output
14 * 9 = 126
12 * 9 = 108
10 * 9 = 90 < (0,3) // two possible results -> (0,9) we need to know which of them so we keep 0, and 3(#iteration)
9 * 9 = 81
8 * 9 = 72
7 * 9 = 63
6 * 9 = 54
5 * 9 = 45
4 * 9 = 36
3 * 9 = 27
2 * 9 = 18
1 * 9 = 9 < (9,12)