A029800 Numbers k such that k, k^2 and k^3 all have the same set of digits.
0, 1, 10, 100, 1000, 10000, 100000, 1000000, 4152760, 9845261, 10000000, 10253497, 10357426, 10384796, 10972365, 12546973, 13247805, 15942760, 16537428, 17534690, 18326705, 18392576, 18492763, 18659437, 19728603, 21648705, 23956714, 24130568, 24351980, 24931756, 27681350
Offset: 1
Examples
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
Links
- David A. Corneth, Table of n, a(n) for n = 1..10001
Programs
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Mathematica
Select[Range[0,2*10^7],Union[IntegerDigits[#]]==Union[ IntegerDigits[ #^2]] == Union[ IntegerDigits[ #^3]]&] (* Harvey P. Dale, Nov 04 2015 *)
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PARI
is(n) = { my(s = Set(digits(n))); s == Set(digits(n^2)) && s == Set(digits(n^3)) } \\ David A. Corneth, Nov 13 2023
Formula
a(n) ~ n. - David A. Corneth, Nov 13 2023
Extensions
More terms from David A. Corneth, Nov 13 2023