which unfortunately does't do anything. I'd like to know why?

Three things are wrong: First of all there's no digit in you input, so [0-9] can't match. Secondly you don't capture the result from [0-9]+, so matching against \1 is bound to fail. Thirdly you can't use a capture as a quantifier, as you already guessed.

Update: Just found that there are actually some 1s in the input. If all sequences are short, you can just generate them:

my $re = join '|', map { qr/\+$_[ACGTNacgtn]{$_}/} 1..20;
s/$re//g;
[download]

Should still be fairly efficient, especially with perl-5.10, which optimizes regex alternations with constant prefixes.

Second update: Added a missing \+ JadeNB++ for noticing.