My first check on code 13 would be to look for a vac leak ,and take the vac line off the Fuel Pressure reg and see if gas comes out that port when at idle.
The car is trying to adapt to an out of wack a/f mix and has reached it's limits, meaning it can not correct . Could also be too high a fuel pressure.
Check the reg first. 02 sesnor could be carboned up from reg and when the car does the AIR test, 02 can not respond to full lean condition of test, so the AIR code follows the 13 code.
Of course , also check that the air pump is coming on., etc.........

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A Dalton