# Python program for OEIS A053918 and A053919
# Michael S. Branicky, May 15 2021

from time import time
time0 = time()

# N.B. "digits" search is to 2*digits of squares of terms 
from itertools import product
from sympy import integer_nthroot
def auptodigs(maxdigits, verbose=False):
  A053918 = []
  A053919 = []
  nextkk = 1
  for d in range(2, maxdigits*2+1):
    for p in product("235", repeat=d):
      kk = int("".join(p))
      if kk < nextkk: continue
      k, ok = integer_nthroot(kk, 2)
      if ok:
        A053918.append(k)
        A053919.append(k*k)
      nextkk = (k+1)**2
    if verbose and d%2 == 0:
      print("done to", d//2, "digits,", time()-time0)
      print("   ", A053918)
      print("   ", A053919)
  return A053918, A053919
print(auptodigs(10, verbose=True)) # ~~~~