%I #23 Jan 17 2024 19:10:26
%S 2,3,7,8,53,77
%N Numbers k such that the decimal digits of k are not present in k^2, k^3, or k^4.
%C No more terms exist below 10^100. The last five digits of any larger term must be 75557, 85557, 88787, 88188, 88988 or 98988. - _Hagen von Eitzen_, Jun 16 2009
%e For k=77, the 1st through 4th powers are {77, 5929, 456533, 35153041}.
%e Digits of k appear first in the 5th powers {32, 243, 16807, 32768, 418195493, 2706784157}.
%t Select[Range[10^3],ContainsNone[IntegerDigits[#],Union[IntegerDigits[#^2],IntegerDigits[#^3],IntegerDigits[#^4]]]&] (* _James C. McMahon_, Jan 17 2024 *)
%Y Cf. A029783, A029790.
%K base,nonn,more
%O 1,1
%A _Labos Elemer_, Feb 28 2005