A188065 Numbers n such that n^3 contains the same digits as some other cube.

5, 8, 35, 38, 50, 80, 101, 102, 110, 178, 196, 201, 221, 227, 257, 258, 279, 289, 319, 329, 331, 341, 345, 350, 355, 356, 371, 379, 380, 384, 405, 406, 408, 417, 427, 455, 457, 473, 497, 500, 514, 553, 564, 576, 635, 638, 639, 641, 644, 656, 665, 668, 674, 689, 709, 711, 722, 725, 773, 781, 792, 800, 804, 836, 858, 862, 894, 923, 933, 943, 961, 973, 978, 981, 983, 992, 996

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

5 is a member since 5^3 = 125, and 512 = 8^3.
178^3 = 5639752 has same digits as 196^3 = 7529536, so 178 and 196 are in the sequence

Maple

dmax:= 10: # to get all terms of at most dmax digits.
N:= 'N':
S:= {}:
for n from 1 while n^3 < 10^dmax do
  w:= sort(convert(n^3, base, 10));
  if assigned(N[w]) then
    if N[w] = 0 then S:= S union {n}
    else
      S:= S union {n, N[w]};
      N[w] = 0
    fi
  else N[w]:= n
  fi
od:
sort(convert(S, list)); # Robert Israel, Jun 15 2017

Mathematica

id3Q[n_]:=Module[{idn3=Sort[IntegerDigits[n^3]], perms}, perms= FromDigits/@ Permutations[idn3]; Length[Select[perms, Sort[IntegerDigits[#]]==idn3 && IntegerQ[#^(1/3)]&]]>1]; Select[Range[1000], id3Q] (* Harvey P. Dale, Apr 27 2012 *)

Prog

(PARI) do(n)=my(v=List()); for(D=1, n, my(m=Map(), low=sqrtnint(10^(D-1)-1, 3)+1, high=sqrtnint(10^D-1, 3), n3, d); for(n=low, high, d=vecsort(digits(n3=n^3)); if(mapisdefined(m, d), mapput(m, d, 1), mapput(m, d, 0))); for(n=low, high, if(mapget(m, vecsort(digits(n^3))), listput(v, n)))); Set(v) \\ Charles R Greathouse IV, Jun 15 2017

Crossrefs

Sequence in context: A275003 A032790 A187997 * A204676 A219947 A075273

Adjacent sequences: A188062 A188063 A188064 * A188066 A188067 A188068

Keyword

nonn,base

Author

Claudio Meller, Mar 20 2011

Status

approved