There is a three-factor in this one.
Multiply 37 by 3, and you have 111.
37 x 3 = 111
Jump up three numbers to 6, and mutliply by 37 again.
You have 222.
37 x 6 = 222
Three more and you are at 9.
Multiply by 37 again and you have 333.
37 x 9 = 333
This "jumpupthree" routine works all the way up to 27
(27 x 37 = 999).
After that, 37 loses its magic.
