ClearAll[SuperD]
SuperD[d_, m_] := Module[{n, res, num},
  res = {};
  n = 1;
  While[Length[res] < m,
   num = IntegerDigits[d n^d];
   If[MatchQ[num, {___, Repeated[d, {d}], ___}],
    AppendTo[res, n]
    ];
   n++;
   ];
  res
  ]
Scan[Print[SuperD[#, 10]] &, Range[2, 6]]