Inheritance, shared primary keys between parent and child tables.

I thought the primary key was NOT shared between parent/child tables through inheritance.

 It seems obvious that the primary key of the parent table is not shared by the child table(am I miss-understanding?)

My experience from playing around with this indicates otherwise.

For example

);

INSERT INTO account_admin(cash) VALUES(12);

My understanding of the documentation is:

SELECT id FROM account_admin;

should return 1,2

actually returns: 1,4;

And:

SELECT id FROM account_user;

should return: 1,2

actually returns: 2,3

While 

SELECT id FROM account;

returns: 1,2,3,4 as expected

Does this mean that child tables of a parent share the same primary key?