(This task is taken from a   Project Euler   problem.)

(All numbers herein are expressed in base ten.)


27   =   128   and   7   is
the first power of   2   whose leading decimal digits are   12.

The next power of   2   whose leading decimal digits
are   12   is   80,

280   =   1208925819614629174706176.



Define        p(L,n)      to be the  nth-smallest
value of    j    such that the base ten representation
of    2j    begins with the digits of    L .

    So   p(12, 1) =  7    and
         p(12, 2) = 80



You are also given that:

         p(123, 45)   =   12710



Task

   find: 
     p(12, 1)  
     p(12, 2)  
     p(123, 45)  
     p(123, 12345)  
     p(123, 678910)  
   display the results here, on this page.


 
p=: adverb define
:
 el =. x
 en =. y
 pwr =. m
 el =. <. | el
 digitcount =. <. 10 ^. el
 log10pwr =. 10 ^. pwr
 'raised found' =. _1 0
 while. found < en do.
  raised =. >: raised
  firstdigits =. (<.!.0) 10^digitcount + 1 | log10pwr * raised
  found =. found + firstdigits = el
 end.
 raised
) 
 