arr = []
for i in 10000:
 i = factorial(i)
 a = []
 while i < 2
  i = sqrt(i)
  a.push(ceil(i))
  a.push(floor(i))
 arr.push(a)

l=[11] # Initial Setup
def f(x): return 1 if x<2 else x*f(x-1)
# factorial
def s(x): return int(x**0.5)
# square root
for i in range(1001): # repeat 1000 times here
    l += list(map(f, l))
    l += list(map(s, l))
    l =  sorted(list(set(l))) # clear duplicates and sort
    print(l) # report

[3, 11, 6317, 39916800]
Traceback (most recent call last):
  File "/usr/local/lib/python3.9/site-packages/IPython/core/interactiveshell.py", line 3444, in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)

a = 1
for i in range(1, 10001):
 a *= i
 b = a
 # Do stuff with factorial

l=[11] # Initial Setup
from math import factorial as f
def s(x): return int(x**0.5)    # square root
def small(x): return x<10001    # Don't get too big and waste time

for i in range(1001): # repeat 1000 times here
    l += list(map(f, l))
    l =  list(filter(small, sorted(list(set(l))))) # clear duplicates and sort
    l += list(map(s, l))
    l =  list(filter(small, sorted(list(set(l))))) # clear duplicates and sort
    print(l) # report

l=[11] # Initial Setup

from math import factorial as f
def square(x):
    # is x a perfect square?
    possible_squareroots = [s(x)+i for i in range(-3,4)]
    return x in [z**2 for z in possible_squareroots]
def s(x): return int(x**0.5)    # square root
def S(x): return s(x) if square(x) else 1+s(x)
def small(x): return x<100001    # Don't get too big and waste time

for i in range(1001): # repeat 1000 times here
    l += list(map(f, l))
    l =  list(filter(small, sorted(list(set(l))))) # clear duplicates and sort