A110815 Least n-digit number m whose square contains only digits not appearing in m.

2, 17, 144, 1447, 14144, 141494, 1414414, 14144134, 141431114, 1414411113, 14143143413, 141431113114, 1414311131114, 14143111141813, 141431113114113, 1414311344113314, 14143111141141113, 141431113114331413

Offset: 1

Author

Lekraj Beedassy, Aug 17 2005

Keywords

• nonn
• base

Comments

floor(sqrt(2)*10^(n-1)) < a(n). - Robert G. Wilson v, Oct 04 2005

Crossrefs

Cf. A110816 (corresponding squares), A112321. Subsequence of A029783.

Programs

Mathematica

f[n_] := Block[{k = Ceiling[10^n*(1/9 + .03032)]}, While[ Intersection[ IntegerDigits[k], IntegerDigits[k^2]] != {}, k++ ]; k]; Table[ f[n], {n, 18}] (* Robert G. Wilson v *)

Python

from math import isqrt
def a(n):
  m = isqrt(int('2'+'0'*(2*n-2)))
  while set(str(m*m)) & set(str(m)) != set(): m += 1
  return m
print([a(n) for n in range(1, 12)]) # Michael S. Branicky, Feb 17 2021

Extensions

a(3) to a(6) corrected, a(7) to a(13) from Klaus Brockhaus, Aug 31 2005; revised Sep 09 2005

a(14)-a(18) from Robert G. Wilson v, Oct 04 2005