For example, I want to keep every 3rd row, but I must keep numbers divisible by 3(or some special rule like that). When I see a number divisible by 3, that restarts the count, meaning I will start counting to 3 from there, unless I see anoter value divisible by 3. Example given below:

import pandas as pd
df = pd.DataFrame.from_dict({'x': [0, 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 14, 17, 20, 23]})
filtered = pd.DataFrame.from_dict({'x': [0, 3,  7,  9,  12,  17]}) # this is the desired dataframe
print (df, 'nn--------------nn', filtered)

     x
0    0
1    1
2    2
3    3
4    4
5    5
6    7
7    8
8    9
9   11
10  12
11  13
12  14
13  17
14  20
15  23 

--------------

     x
0   0
1   3
2   7
3   9
4  12
5  17