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Numbers k such that k, k^2 and k^3 all have the same set of digits.
6

%I #34 Jul 03 2024 13:34:06

%S 0,1,10,100,1000,10000,100000,1000000,4152760,9845261,10000000,

%T 10253497,10357426,10384796,10972365,12546973,13247805,15942760,

%U 16537428,17534690,18326705,18392576,18492763,18659437,19728603,21648705,23956714,24130568,24351980,24931756,27681350

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

%H David A. Corneth, <a href="/A029800/b029800.txt">Table of n, a(n) for n = 1..10001</a>

%F a(n) ~ n. - _David A. Corneth_, Nov 13 2023

%e 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 Select[Range[0,2*10^7],Union[IntegerDigits[#]]==Union[ IntegerDigits[ #^2]] == Union[ IntegerDigits[ #^3]]&] (* _Harvey P. Dale_, Nov 04 2015 *)

%o (PARI)

%o is(n) = {

%o my(s = Set(digits(n)));

%o s == Set(digits(n^2)) && s == Set(digits(n^3))

%o } \\ _David A. Corneth_, Nov 13 2023

%Y Cf. A029801, A029802.

%Y Cf. A011557 (a subsequence).

%K nonn,base

%O 1,3

%A _Patrick De Geest_

%E More terms from _David A. Corneth_, Nov 13 2023