(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.


Module Module1
 
    Function Func(ByVal l As Integer, ByVal n As Integer) As Long
        Dim res As Long = 0, f As Long = 1
        Dim lf As Double = Math.Log10(2)
        Dim i As Integer = l
 
        While i > 10
            f *= 10
            i /= 10
        End While
 
        While n > 0
            res += 1
 
            If CInt((f * Math.Pow(10, res * lf Mod 1))) = l Then
                n -= 1
            End If
        End While
 
        Return res
    End Function
 
    Sub Main()
        Dim values = {Tuple.Create(12, 1), Tuple.Create(12, 2), Tuple.Create(123, 45), Tuple.Create(123, 12345), Tuple.Create(123, 678910), Tuple.Create(99, 1)}
        For Each pair In values
            Console.WriteLine("p({0,3}, {1,6}) = {2,11:n0}", pair.Item1, pair.Item2, Func(pair.Item1, pair.Item2))
        Next
    End Sub
 
End Module