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Cubes that have some nontrivial permutation of digits that is also a cube.
1

%I #13 Nov 13 2015 12:01:36

%S 125,512,42875,54872,125000,512000,1030301,1061208,1331000,5639752,

%T 7529536,8120601,10793861,11697083,16974593,17173512,21717639,

%U 24137569,32461759,35611289,36264691,39651821,41063625,42875000,44738875

%N Cubes that have some nontrivial permutation of digits that is also a cube.

%C Leading zeros are not allowed.

%H Robert Israel, <a href="/A034290/b034290.txt">Table of n, a(n) for n = 1..10000</a>

%e 125 and 512 are both in the sequence because 5^3 = 125 and 8^3 = 512.

%p S:= {}:

%p for x from 1 to 10^3 do

%p L:= sort(convert(x^3,base,10));

%p if assigned(R[L]) then S:= S union {x^3, R[L]}

%p else R[L]:= x^3

%p fi

%p od:

%p sort(convert(S,list)); # _Robert Israel_, Nov 12 2015

%t Select[Range[360]^3, AnyTrue[Rest[FromDigits /@ Permutations@ IntegerDigits@ #], Function[x, IntegerQ@ Power[x, 1/3] && IntegerLength@ x == IntegerLength@ #]] &] (* _Michael De Vlieger_, Nov 12 2015 *)

%K nonn,base

%O 1,1

%A _Erich Friedman_