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.


# To take advantage of gojq's arbitrary-precision integer arithmetic:
def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);
 
# Input is $d, the number of consecutive digits, 2 <= $d <= 9
# $max is the number of superd numbers to be emitted.
def superd($number):
  . as $d
  | tostring as $s
  | ($s * $d) as $target
  | {count:0, j: 3 }
  |  while ( .count <= $number;
        .emit = null
        | if ((.j|power($d) * $d) | tostring) | index($target)
          then .count += 1
          | .emit = .j
	  else .
          end 
        | .j += 1 )
   | select(.emit).emit ;
 
# super-d for 2 <=d < 8
range(2; 8)
| "First 10 super-\(.) numbers:",
   superd(10)