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.


import "/big" for BigInt
import "/fmt" for Fmt
 
var start = System.clock
var rd = ["22", "333", "4444", "55555", "666666", "7777777", "88888888"]
for (i in 2..8) {
    Fmt.print("First 10 super-$d numbers:", i)
    var count = 0
    var j = BigInt.three
    while (true) {
        var k = j.pow(i) * i
        var ix = k.toString.indexOf(rd[i-2])
        if (ix >= 0) {
            count = count + 1
            Fmt.write("$i ", j)
            if (count == 10) {
                Fmt.print("\nfound in $f seconds\n", System.clock - start)
                break
            }
        }
        j = j.inc
    }
}