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.


function superd(N)
    println("First 10 super-$N numbers:")
    count, j = 0, BigInt(3)
    target = Char('0' + N)^N
    while count < 10
        if occursin(target, string(j^N * N))
            count += 1
            print("$j ")
        end
        j += 1
    end
    println()
end
 
for n in 2:9
    @time superd(n)
end
 