# Python code for OEIS A262713
# Michael S. Branicky, Aug 19 2021

# A262713		Numbers n such that sum of digits on n^2 is 10.		1
data = [8, 19, 35, 46, 55, 71, 80, 145, 152, 179, 190, 251, 332, 350, 361, 449, 451, 460, 548, 550, 649, 710, 800, 1450, 1520, 1790, 1900, 2510, 3320, 3500, 3610, 4490, 4499, 4510, 4600, 5480, 5500, 6490, 7100, 8000, 14500, 15200, 17900, 19000, 20249, 20251, 24499]

from time import time
time0 = time()

def cond_final(s): return sum(map(int, s)) == 10
def cond_inter(s): return sum(map(int, s)) < 10

alst = []
digits = "0123456789"
digset = set(digits)
valid = set([""])

for e in range(1, 1001):
  print("Starting with", e, "digits; # to test =", len(valid), time()-time0)
  newvalid = set()
  for tstr in valid:
    for d in digset:
      dtstr = d + tstr
      dt = int(dtstr)
      remstr = str(dt**2)[-e:]
      if cond_inter(remstr):
        newvalid.add(dtstr)
        if cond_final(str(dt**2)):
            alst.append(dt)
            alst = sorted(set(alst))
  print("# Terms =", len(alst))
  print("   alst =", alst)
  print("   data =", data)
  with open('b262713.txt', 'w') as bfile:
    for n, an in enumerate(alst, start=1):
      bfile.write(f"{n} {an}\n")          
  valid = newvalid