I have gotten the following to work:
for i in {2..10} do echo \"output: $i\" done
It produces a bunch of lines of output: 2
output: 2
Brace expansion, {x..y} is performed before other expansions, so you cannot use that for variable length sequences.
Instead, use the seq 2 $max method as user mob stated.
seq 2 $max
So, for your example it would be:
max=10 for i in `seq 2 $max` do echo "$i" done