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A124651 Least n-digit number m such that m and m^10 are zeroless. 1
1, 12, 113, 1134, 11227, 112154, 1112236, 11111566, 111123685, 1111133874, 11111178192, 111111796422, 1111111392823, 11111112811396, 111111112641445, 1111111115954155, 11111111158315794, 111111111132821544, 1111111111273944122, 11111111111777673838, 111111111113343756694 (list; graph; refs; listen; history; text; internal format)
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: A153882 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

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Last modified July 26 10:35 EDT 2021. Contains 346294 sequences. (Running on oeis4.)