Let's see if I can work this out correctly;
First assume the spaceships weight negligibly different than the mass of the fuel. The thrust needed to push the weight at a steady 1g will be proportional to the mass of the ship at each interval of time. SO the rate of mass burn is proportional to the mass which means the mass is a decaying exponential.
M = Mo * exp( -g * time / thrust_to_weight )
If you think about this for a moment it becomes clear that any amount of mass would do since as the mass gets lighter it takes less fuel so the ship could go indefinitely at 1g. The problem is the assumption that the ship weighs nothing. so let's fix that.
dM/dt = -g*(M+Ms)/thrust_to_weight.
where Ms = mass of ship and M = mass of fuel.
I'm spacing on how to solve that equation so I'll approximate it by saying that until M = Ms we can mostly ignore the ship mass. therfore for a 6.6 year flight time the fuel required is about:
Mfuel = Ms * exp( g* (6.6 years)/thrust_to_weight )
Mfule = Ms * exp( +303,800,000/thrust_to_weight).
So you need a rather high thrust to weight ratio due to the coefficient in the exponetial.
Let the pillory for my "obvious" math errors begin!