We noticed this, too, with GoogleBot in DNN 4.9.x. This is probably caused by the DotNetNuke.UI.WebControls.CaptchaControl.Decrypt() method. When the session has expired, the routine returns the empty string. It's caller, CaptchaControl.GenerateImage() does not check the return value it receives from Decrypt():

Friend Shared Function GenerateImage(ByVal encryptedText As String) As Bitmap
            Dim encodedText As String = Decrypt(encryptedText)
            Dim bmp As Bitmap = Nothing
            Dim Settings As String() = Split(encodedText, _Separator)

            Try
                Dim width As Integer = Integer.Parse(Settings(0)) ' <-- exception originates here
                '' ... omitted for brevity ...
            Catch exc As Exception
                LogException(exc) ' <-- and gets logged here
            End Try

            Return bmp
End Function

It's definitely safe to ignore this error, as it just means that an attempt was made to generate a CAPTCHA image for an expired session. However, we see *lots* of these errors, so I think I'll try the robots.txt solution that Mitchel Sellers suggested.