A124651 Least n-digit number m such that m and m^10 are zeroless.

1, 12, 113, 1134, 11227, 112154, 1112236, 11111566, 111123685, 1111133874, 11111178192, 111111796422, 1111111392823, 11111112811396, 111111112641445, 1111111115954155, 11111111158315794, 111111111132821544, 1111111111273944122, 11111111111777673838, 111111111113343756694

Offset

1,2

Comments

a(n)^10 is converging to 2867971991..1 (1 repeated 10*n-18 times at end), or 10^(10*n-10) times the smallest rational greater than (10/9)^10 that contains no 0 digit. - Michael S. Branicky, Jan 12 2021

Links

Michael S. Branicky, Table of n, a(n) for n = 1..25

Example

12^10 is 61917364224 but 10 and 11^10 = 25937424601 have zeros. - Michael S. Branicky, Jan 12 2021

Prog

(Python)
from sympy import integer_nthroot
def a(n):
  if n == 1: return 1
  m, perfect = integer_nthroot(int('286797199' + '1'*(10*n-18)), 10)
  strm = str(m)
  # strm = "1"*n # slower than the foregoing for larger n
  while strm.count('0') > 0 or str(m**10).count('0') > 0:
    if '0' in strm:
      ind0 = strm.find('0')
      m = int(strm[:ind0] + '1'*(len(strm)-ind0))
    elif strm[-1] == '9':
      m += 2
    else:
      m += 1
    strm = str(m)
  return m
for n in range(1, 15):
  print(a(n), end=", ") # Michael S. Branicky, Jan 12 2021

Crossrefs

Sequence in context: A357650 A322649 A198375 * A231379 A237855 A055287

Adjacent sequences: A124648 A124649 A124650 * A124652 A124653 A124654

Keyword

base,nonn

Author

Zak Seidov, Dec 22 2006

Extensions

a(17) and beyond from Michael S. Branicky, Jan 12 2021

Status

approved