perl -i.bak -nle 's/search/replace/g unless $. & 2; print' file

Your one-liner is not going to do what you think. $. & 2 is going to evaluate to true whenever the third second bit from the right (2 is binary 100) is set. Given this input file (lines.txt)

line 1
line 2
line 3
line 4
line 5
line 6
line 7
line 8
line 9
[download]

adapting your one-liner to just print the lines gives

$ perl -nle 'print unless $. & 2;' lines.txt
line 1
line 4
line 5
line 8
line 9
[download]

Did you actually test your adaptation of GrandFather's idea before posting? Changing between odd and even is as simple as if $. & 1 and unless $. & 1. Perhaps you could have a look at "Bitwise And" in perlop to further your understanding.

Cheers,

JohnGG

Update: Corrected typo.

Update 2: Corrected huge balls-up, thanks fenLisesi. Where did I get "2 is binary 100" from?

Update 3: And thanks clinton, saw your reply after /msg from fenLisesi

you missed another typo - 2 is binary 10, not 100

To flesh out the reasoning:

   DECIMAL          BINARY               TRUE / FALSE
   =============    =================    ============
   0  & 2  == 0     000 & 010  == 000    FALSE
   1  & 2  == 0     001 & 010  == 000    FALSE
   2  & 2  == 2     010 & 010  == 010    TRUE
   3  & 2  == 2     011 & 010  == 010    TRUE
   4  & 2  == 0     100 & 010  == 000    FALSE
   5  & 2  == 0     101 & 010  == 000    FALSE
   6  & 2  == 2     110 & 010  == 010    TRUE
   7  & 2  == 2     111 & 010  == 010    TRUE
[download]

Clint

Yes, I've gone bright red :(