Where mysql writes its log seqeunce numbers and last checkpoint at?
Well, that is handled in memory and transactionally stored on disk on the transaction log (by default, the ib_logfile0 and i_blogfile1. But if you just want to know its value, you can check SHOW ENGINE INNODB STATUS or simply:

mysql&gt; SHOW GLOBAL STATUS like '%lsn%';
+----------------------------+-------------+
| Variable_name              | Value       |
+----------------------------+-------------+
| Innodb_lsn_current         | 25808994907 |
| Innodb_lsn_flushed         | 25808994907 |
| Innodb_lsn_last_checkpoint | 25808994907 |
+----------------------------+-------------+
3 rows in set (0.00 sec)


If you want MySQL to output that periodically to its error log, you can enable one of the InnoDB monitors.