Well what you need to do is as following --

1. Create a Sequence (let's say log_seq)
2. Create a database Startup Trigger that will increment the sequence whenever the database is brought up --

create or replace trigger t1 after startup on database
...code to increment the sequence...something like ...SELECT log_seq.NextVal INTO :x from DUAL;

3. In your Update trigger (logon_trg and logof_trg) you need to use the log_Seq.CurrVal to insert/compare the current value of the Sequence.

- Rajeev