Sum of pairs from list: memoization, design optimalization

From a list of integers and a single sum value, I have to return the first two values in order of appearance that adds up to the sum. source of the task

I think the most optimal way to scan the list is:

1. index 0, index 1
   

2. index 0,          index 2
   

3.          index 1, index 2
   

4. index 0,                   index 3
   

5.         index 1,           index 3
   

6.                   index 2, index 3
   

and so on. Am I right so far?

Then I used memoization to cut numbers appearing more than twice.

The code I wrote is functional but times-out on the more advanced tests. Here it is:

def sum_pairs(ints, s):
d={}
n2_index = 0
d[ints[0]] = 1
while True:
    n2_index += 1
    if ints[n2_index] not in d.keys():
        d[ints[n2_index]] = 0
        
    if d[ints[n2_index]] == 2:
        if n2_index == len(ints)-1:
            return None
        continue
    for n1_index in range (0, n2_index):

        if ints[n1_index] + ints[n2_index] == s:
            return [ints[n1_index], ints[n2_index]]
    
    d[ints[n2_index]] += 1
    
    if n2_index == len(ints)-1:
        return None

I would appreciate it greatly if you could help me understand my mistake/mistakes and how to approach this kind of task. Cheers!