My inverter installation instructions said 300 amps. Don't forget the energy lost to invert to A/C and voltage drop on a loaded alternator. As you get to the limit of the alternator, the voltage will drop off, current requirement will then increase to maintain AC power.
When using my snow plow, the hydraulic pump can draw near 200Amps when the pressure is dead headed and the pressure relief valve opens. My voltage drops from 14.5 to below 13v.
Don't forget to factor in 20 amps or more to run the truck too.
I haven't run my inverter at full load, so I don't know what current it takes.
I bought the inverter from a buddy that tried to run his camper with it and a couple 8D's (1100 to 1400cca). He bought a 3kw generator.
All BS aside.
You need to find the installation instructions for the inverter you plan to use.
I found a random manual for a wagan tech 3kW inverter, (google search - wagan 3000 watt inverter instructions) page 6:
At 3,000 watts continuous output this inverter requires a DC power supply (battery bank)
that can continuously supply 300 amps at 12VDC for the duration of the run time
3000w/12v = 250a so why the extra 50A?
It also covers configuring a battery bank. They noted, CCA is meaniless for inverters, Ah (amp hours) and knowing the battery derating factor is key.
Their example talks about needing 1500 watts for 10hours, which will require 150 amps of current for 10 hours. The batteries required to provide this requirement after derating was 16,500 Ah of capacity.
Do some research.
Good luck.