@Singleton
@LocalBean
@WebListener
public class SessionBean implements HttpSessionListener {

    private static final Logger log = Logger.getLogger(SessionBean.class.getSimpleName());
    private static final HashMap<SessionBean, Integer> map = new HashMap<>();
    private static int number = 0;
    private int counter = 0;

    @PostConstruct
    public void appStartup() {
        Integer num = (++number);
        boolean newInstance = (map.put(this, num) == null);
        log.log(Level.INFO, "SessionBean({0}){1}", new Object[]{num, (newInstance ? " new!" : "")});
    }

    @PreDestroy
    public void appShutdown() {
        log.log(Level.INFO, "~SessionBean({0})", map.get(this));
    }

    public int getNum() {
        return map.get(this);
    }

    public int getCounter() {
        return counter;
    }

    @Override
    public void sessionCreated(HttpSessionEvent se) {
        log.log(Level.INFO, "sessionCreated({0}) {1}", new Object[]{map.get(this), se.getSession().getId()});
        counter++;
    }

    @Override
    public void sessionDestroyed(HttpSessionEvent se) {
        log.log(Level.INFO, "sessionDestroyed({0}) {1}", new Object[]{map.get(this), se.getSession().getId()});
        counter--;
    }
}

@WebServlet(name = "Servlet1", urlPatterns = {"/Servlet1"})
public class Servlet1 extends HttpServlet {

    @EJB
    private SessionBean sessionBean;

    @Override
    protected void doGet(HttpServletRequest request, HttpServletResponse response)
            throws ServletException, IOException {
        request.getSession(true);
        try (PrintWriter out = response.getWriter()) {
            out.println("Bean(" + sessionBean.getNum() + ") has count: " + sessionBean.getCounter());
        }
    }
}