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.


Imports System.Numerics
 
Module Module1
 
    Sub Main()
        Dim rd = {"22", "333", "4444", "55555", "666666", "7777777", "88888888", "999999999"}
        Dim one As BigInteger = 1
        Dim nine As BigInteger = 9
 
        For ii = 2 To 9
            Console.WriteLine("First 10 super-{0} numbers:", ii)
            Dim count = 0
 
            Dim j As BigInteger = 3
            While True
                Dim k = ii * BigInteger.Pow(j, ii)
                Dim ix = k.ToString.IndexOf(rd(ii - 2))
                If ix >= 0 Then
                    count += 1
                    Console.Write("{0} ", j)
                    If count = 10 Then
                        Console.WriteLine()
                        Console.WriteLine()
                        Exit While
                    End If
                End If
 
                j += 1
            End While
        Next
    End Sub
 
End Module