All right. If we start with G(0) as first therm it would be G(9) which would be after the formula I pointed out in another comment
2018=21a+34b 
again 2018 mod 55 is 38 2018-38=1980 1980/55=36
so the a has to be 36 or less.
2018-21a=34b
1009-21a/2=17b
a/2=c-> cmax=18
(1009-21c)/17=b

for a+b minimal a has to be as small as posible since b has a bigger impact (2ax=34 x has to be bigger than 1.5)
So you can either make a table or test for each number for c beginning at 1 and stopping as soon as b is an integer.
I dicided to go with the last option. I won't post the boring calculations.
It turns out it works for c=10 and so b is 47 and a is 20.
I checked even further and it turns out there is no other possible pair smaler than c=18 and if c larger 18 a smaller b would not apply.