2006 Mazda 06 V6 started choking down sputtering, and minor backfire. This all started just before the car ran out of gas. Put in gas but no changes.

Took car to repair shop and they think it might be catalytic converter.

It did show those same symptoms a few weeks ago with a half a tank of gas.

I am thinking perhaps the fuel pump/filter needs changing.

No check engine lights are on

 

UPDATE. Took to mechanic and he checked it out. Could not find anything wrong.
This was after the car set overnite and was cool the next morning. So, apparently it only happens when the motor is warm/hot

All 3 coils changed and tune up about 4 months ago

 

3 coils? 4 or 6 cyl? I'll guess 6 because the back 3 are buried and not serviceable unless you remover the upper intake.

Next thing to look at would be the fuel pump. If your in the USA, there is no filter to replace. Since you have a older 6 and ran it dry once, I would check both pressure and volume with the engine hot. Fuel pumps rely on fuel to keep them cool. Running an older pump dry may have taken it's toll.

 

It has been at the dealer for 2 days and they cannot find the problem

 

Which motor do you have in your 6?