What output does the following Bash script produce?

a$=1$

while $[$ a $-$lt $3]$

do

echo $a

a $=$ $$(($a $+1))$

done

What output does the following Bash script produce?

a$=1$

while $[$ a $-$lt $3]$

do

echo $a

a $=$ $$(($a $+1))$

done

outputs the numbers $2$ and $3$ to the display

outputs the numbers $1$ and $2$ to the display

None, there is a syntax error that prevents the script from running.

outputs the numbers $1,2,$ and $3$ to the display