Pandas MultiIndex match on one index level

I have a pandas MultiIndex object where the first level is a regular increasing index of ints, and the second level contains other integers that may or may not repeat for different 'frst' index values:

lst = list(filter(lambda x: x[1]%5 == x[0] or x[1]%4 == x[0],[(i,j) for i in range(5) for j in range(0, 20, 2)]))
mi = pd.MultiIndex.from_tuples(lst).rename(['frst', 'scnd'])
# mi = MultiIndex([(0,  0),(0,  4),(0,  8),(0, 10),(0, 12),(0, 16),(1,  6),(1, 16),(2,  2),(2,  6),(2, 10),(2, 12),(2, 14),(2, 18),(3,  8),(3, 18),(4,  4),(4, 14)], names=['frst', 'scnd'])

For a given frst value (e.g. frst_idx = 0) and some shift, I need to find all indices where frst is frst_idx+shift, and scnd is shared between frst_idx and frst_idx+shift.

So for example:

frst_idx = 0, shift = 3 should output [8] because the MultiIndex above contains both (0, 8) and (3, 8).
frst_idx = 1, shift = 1 should output [6] because (1, 6) and (2, 6) are both in the index

So I'm hoping for a function that can take these args and return a pd.Series of all matching scnd values:

my_func(multi_index=mi, frst_idx=0, shift=3) ==> pd.Series([8])

Doing this iteratively is very expensive (O(n^2)), I'm hoping there's some pandas magic to do this faster.

Solution

I found the following solution:

# reminder: $mi is a MultiIndex, mi.names = ['frst', 'scnd']
# assume some integer values for $frst_idx1, $shift

scnd_indices1 = mi[mi.get_level_values('frst') == frst_idx1].drop_level('frst')

frst_idx2 = frst_idx1 + shift
scnd_indices2 = mi[mi.get_level_values('frst') == frst_idx2].drop_level('frst')

result = scnd_indices1.intersection(scnd_indices2).to_series().reset_index(drop=True)