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

1,3

Links

David A. Corneth, Table of n, a(n) for n = 1..10001

Formula

a(n) ~ n. - David A. Corneth, Nov 13 2023

Example

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

Mathematica

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

Prog

(PARI)
is(n) = {
   my(s = Set(digits(n)));
   s == Set(digits(n^2)) && s == Set(digits(n^3))
} \\ David A. Corneth, Nov 13 2023

Crossrefs

Cf. A029801, A029802.

Cf. A011557 (a subsequence).

Sequence in context: A135654 A219112 A232661 * A232662 A168070 A263019

Adjacent sequences: A029797 A029798 A029799 * A029801 A029802 A029803

Keyword

nonn,base

Author

Patrick De Geest

Extensions

More terms from David A. Corneth, Nov 13 2023

Status

approved