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A054037
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Numbers k such that k^2 contains exactly 9 different digits.
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14
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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MAPLE
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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;
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MATHEMATICA
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okQ[n_] := Module[{n2=n^2}, Max[DigitCount[n2, 10]]==1 && IntegerLength[n2]==9]; Select[Range[20000], okQ] (* Harvey P. Dale, Mar 20 2011 *)
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PROG
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(Python)
from itertools import count, islice
def agen(): yield from (k for k in count(10**4) if len(set(str(k*k)))==9)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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