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A054037
Numbers k such that k^2 contains exactly 9 different digits.
14
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
1,1
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)
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 *)
PROG
(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
KEYWORD
nonn,base
AUTHOR
Asher Auel, Feb 28 2000
STATUS
approved