How to replicate col = col + 1

Firstly. While the rule that you never update a primary key may be a philosophical choice in a non-replicated system, it is an architectural requirement of a replicated system.

If you use simple data replication, and your primary table is:

id
---
1
2
3

and you issue a:

update table set id=id+1

Rep server will do this in the replicate:

begin tran
update table set id=2 where id=1
update table set id=3 where id=2
update table set id=4 where id=3
commit tran

Hands up all who can see a bit of a problem with this! Remember, repserver doesn't replicate statements, it replicates the results of statements.

One way to perform this update is to build a stored procedure on both sides that executes the necessary update and replicate the stored procedure call.