I need an auto increment for the PK such that if the table's primary keys are
1, 2, 3, 4, 5, 6
1, 2, 3, 6
No - AutoIncrement is intentionally designed to keep IDs unique at the risk of not being sequential.
I would even avoid using triggers or something to "pack" the missing numbers - you run the risk of two processes trying to insert the same number, performance problems by inserting in the middle of your (presumably) clustered index, etc.
If you're concerned about running out of values, use
bigint - it can store 9 trillion trillion values - more than you'd ever be able to consume even if you deleted millions of records a day.