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

1,1

Comments

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

Links

Table of n, a(n) for n=1..18.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A037741 A037636 A163066 * A273340 A074624 A374377

Adjacent sequences: A110812 A110813 A110814 * A110816 A110817 A110818

Keyword

nonn,base

Author

Lekraj Beedassy, Aug 17 2005

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

Status

approved