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.


from itertools import islice, count
 
def superd(d):
    if d != int(d) or not 2 <= d <= 9:
        raise ValueError("argument must be integer from 2 to 9 inclusive")
    tofind = str(d) * d
    for n in count(2):
        if tofind in str(d * n ** d):
            yield n
 
if __name__ == '__main__':
    for d in range(2, 9):
        print(f"{d}:", ', '.join(str(n) for n in islice(superd(d), 10)))