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A029800 Numbers k such that k, k^2 and k^3 all have the same set of digits.

%I A029800 #34 Jul 03 2024 13:34:06
%S A029800 0,1,10,100,1000,10000,100000,1000000,4152760,9845261,10000000,
%T A029800 10253497,10357426,10384796,10972365,12546973,13247805,15942760,
%U A029800 16537428,17534690,18326705,18392576,18492763,18659437,19728603,21648705,23956714,24130568,24351980,24931756,27681350
%N A029800 Numbers k such that k, k^2 and k^3 all have the same set of digits.
%H A029800 David A. Corneth, <a href="/A029800/b029800.txt">Table of n, a(n) for n = 1..10001</a>
%F A029800 a(n) ~ n. - _David A. Corneth_, Nov 13 2023
%e A029800 9845261 is in the sequence as 9845261 has digits {1, 2, 4, 5, 6, 8, 9}, 9845261^2 = 96929164158121 has digits {1, 2, 4, 5, 6, 8, 9} as does 9845261^3 = 954292919648546514581. - _David A. Corneth_, Nov 13 2023
%t A029800 Select[Range[0,2*10^7],Union[IntegerDigits[#]]==Union[ IntegerDigits[ #^2]] == Union[ IntegerDigits[ #^3]]&] (* _Harvey P. Dale_, Nov 04 2015 *)
%o A029800 (PARI)
%o A029800 is(n) = {
%o A029800    my(s = Set(digits(n)));
%o A029800    s == Set(digits(n^2)) && s == Set(digits(n^3))
%o A029800 } \\ _David A. Corneth_, Nov 13 2023
%Y A029800 Cf. A029801, A029802.
%Y A029800 Cf. A011557 (a subsequence).
%K A029800 nonn,base
%O A029800 1,3
%A A029800 _Patrick De Geest_
%E A029800 More terms from _David A. Corneth_, Nov 13 2023