A112321 -id:A112321 - cp's OEIS frontend

A112322 Exclusionary square associated to corresponding smallest n-digit number (A112321), or 0 if no such number exists.

Original entry on oeis.org

4, 289, 24649, 2393209, 227828836, 41566646641, 0, 0, 0

Offset: 1

Lekraj Beedassy and Klaus Brockhaus, Sep 08 2005

m has an exclusionary square if m consists of distinct digits and m^2 is made up only of digits not appearing in m.

Cf. A112321, A110816.

A112736 Numbers whose square is exclusionary.

Original entry on oeis.org

2, 3, 4, 7, 8, 9, 17, 18, 24, 29, 34, 38, 39, 47, 53, 54, 57, 58, 59, 62, 67, 72, 79, 84, 92, 94, 157, 158, 173, 187, 192, 194, 209, 237, 238, 247, 253, 257, 259, 307, 314, 349, 359, 409, 437, 459, 467, 547, 567, 612, 638, 659, 672, 673, 689, 712, 729, 738, 739, 749

Offset: 1

Lekraj Beedassy, Sep 16 2005

The number m with no repeated digits has an exclusionary square m^2 if the latter is made up of digits not appearing in m. For the corresponding exclusionary squares see A112735.

a(49) = 567 and a(68) = 854 are the only two numbers k such that the equation k^2 = m uses only once each of the digits 1 to 9 (reference David Wells). Exactly: 567^2 = 321489, and, 854^2 = 729316. - Bernard Schott, Dec 20 2021

			409^2 = 167281 and the square 167281 is made up of digits not appearing in 409, hence 409 is a term.

H. Ibstedt, Solution to Problem 2623, "Exclusionary Powers", pp. 346-9, Journal of Recreational Mathematics, Vol. 32 No.4 2003-4 Baywood NY.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, 1997, page 144, entry 567.

Giovanni Resta, Table of n, a(n) for n = 1..142 (full sequence)

Cf. A000290, A112321, A112735.

This is a subsequence of A029783 (Digits of n are not present in n^2) of numbers with all different digits. The sequence A059930 (Numbers n such that n and n^2 combined use different digits) is a subsequence of this sequence.

Select[Range[1000], Intersection[IntegerDigits[ # ], IntegerDigits[ #^2]] == {} && Length[Union[IntegerDigits[ # ]]] == Length[IntegerDigits[ # ]] &] (* Tanya Khovanova, Dec 25 2006 *)

More terms from Tanya Khovanova, Dec 25 2006

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

Original entry on oeis.org

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

Offset: 1

Lekraj Beedassy, Aug 17 2005

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

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

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 *)

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

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

cp's OEIS Frontend

A112322 Exclusionary square associated to corresponding smallest n-digit number (A112321), or 0 if no such number exists.

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A112736 Numbers whose square is exclusionary.

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

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