A054037 Numbers k such that k^2 contains exactly 9 different digits.

10124, 10128, 10136, 10214, 10278, 11826, 12363, 12543, 12582, 12586, 13147, 13268, 13278, 13343, 13434, 13545, 13698, 14098, 14442, 14676, 14743, 14766, 15353, 15681, 15963, 16549, 16854, 17252, 17529, 17778, 17816, 18072, 19023, 19377, 19569, 19629, 20089

Offset: 1

Author

Asher Auel, Feb 28 2000

Keywords

• nonn
• base

Comments

There are three prime numbers {13147, 20089, 21397} and corresponding squares {172843609, 403567921, 457831609} necessarily contain zero (otherwise n and n^2 are divisible by 3). - Zak Seidov, Jan 18 2012

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..10000 (terms 1..83 from Zak Seidov)

Crossrefs

Cf. A016069, A054031, A054032, A054033, A054034, A054035, A054036, A054038, A054039, A156977.

Programs

Maple

f := []; for i from 0 to 200 do if nops({op(convert(i^2,base,10))})=9 then f := [op(f),i] fi; od; f;

Mathematica

okQ[n_] := Module[{n2=n^2}, Max[DigitCount[n2,10]]==1 && IntegerLength[n2]==9]; Select[Range[20000], okQ]  (* Harvey P. Dale, Mar 20 2011 *)

Python

from itertools import count, islice
def agen(): yield from (k for k in count(10**4) if len(set(str(k*k)))==9)
print(list(islice(agen(), 37))) # Michael S. Branicky, May 24 2022