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[buran]

Reading your question a second time, I see that most likely I was wrong as to how the file looks like
I see that in your file numbers are on the same line.
In this case the problem is if not(str(k)) in numer:`

here not(str(k)) is False always. And you condition is actually if False in numer: - which is always evaluated False

Note that you approach is prone to errors e.g. you have 12 in your file. the way you check, even if you fix the condition, will eleminate also 1 and 2 (although 2 is present also separately).

>>> '1' in '2 4 9 12 8 3\n'
True

file:

Output:
2 4 9 12 8 3

import random
fname = "bjjj.txt"
with open(fname) as f:
    numbers = f.readline().strip().split()
# print the numbers in the file:
print(numbers)
for _ in range(15): # loop 15 times
    k = str(random.randint(1, 16))
    if k not in numbers:
        print (f'{k} não EXISTE')
        numbers.append(k)
    else:
        print (f'{k} EXISTE')
with open(fname, 'w') as f: # open file in write mode
    f.write(f'{" ".join(numbers)}\n')