Well you can use to_char() function in the select clause but, you will need to select all the a.num field separately and not with *.
And in postgresql you will need to specify a mask for to_char()function, so it would be to_char(field, mask), for example we can supply 'FM999999999999999999' as a mask to accept the maximum possible digits.
Your query would be something like this:
Select *, to_char(a.num, 'FM999999999999999999') as num from A a WHERE num LIKE '%345%'
You can take a look at Postgresql Data Type Formatting Functions for further details.
To write the query in your code with EntityManager you can create a native query using .createNativeQuery() method, this is how should be your code:
em.createNativeQuery("Select *, to_char(a.num, 'FM999999999999999999') as num from A a WHERE num LIKE '%345%'");