A super-d number is a positive, decimal (base ten) integer   n   such that   d × nd   has at least   d   consecutive digits   d   where

   2 ≤ d ≤ 9

For instance, 753 is a super-3 number because 3 × 7533 = 1280873331.


Super-d   numbers are also shown on   MathWorld™   as   super-d    or   super-d.



Task

 Write a function/procedure/routine to find super-d numbers.
 For   d=2   through   d=6,   use the routine to show the first   10   super-d numbers.


Extra credit

 Show the first   10   super-7, super-8, and/or super-9 numbers   (optional).


See also

   Wolfram MathWorld - Super-d Number.
   OEIS: A014569 - Super-3 Numbers.


for d = 2, 5 do
  local n, found = 0, {}
  local dds = string.rep(d, d)
  while #found < 10 do
    local dnd = string.format("%15.f", d * n ^ d)
    if string.find(dnd, dds) then found[#found+1] = n end
    n = n + 1
  end
  print("super-" .. d .. ":  " .. table.concat(found,", "))
end