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.


 
// Generate Super-N numbers. Nigel Galloway: October 12th., 2019
let superD N=
  let      I=bigint(pown 10 N)
  let      G=bigint N
  let      E=G*(111111111I%I)
  let rec fL n=match (E-n%I).IsZero with true->true |_->if (E*10I)<n then false else fL (n/10I)
  seq{1I..999999999999999999I}|>Seq.choose(fun n->if fL (G*n**N) then Some n else None)
 