Imports System
Imports System.Math
Module LeadingDigits
' return true if 2^n starts with prefix, else false
Function startsWithPrefix(n As Long, prefix As Integer) As Boolean
Dim log2v As Double = Log10(2.0)
Dim x As Double = n * log2v
Dim frac As Double = x - Floor(x)
' count digits in prefix
Dim buf As String = prefix.ToString()
Dim digits As Integer = buf.Length
' compute leading digits
Dim leading As Integer = CInt(Floor(Pow(10, frac + digits - 1)))
Return leading = prefix
End Function
Sub Main()
Dim prefix As Integer = 12
Dim n As Long = 1
While True
If startsWithPrefix(n, prefix) Then
Console.WriteLine("First n = " & n)
Console.WriteLine("2 ^ " & n & " = " & CInt(Pow(2, n)))
Exit While
End If
n += 1
End While
End Sub
End Module
' run:
'
' First n = 60
' 2 ^ 60 = 128
'
