foreach my $checked (@chk_acc) 
     {
       chomp();
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chomp() is short for chomp( $_ ) but you don't assign any value to $_ so the use of chomp there is superfluous.

       if($checked=~/^(\w{3})(\d{4,7})/ig)
        {
          # it should print the accounts starting with letters here
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The \w character class matches all upper case letters and all lower case letters and all digits and the '_' character so the use of the /i option is superfluous and the comment is wrong because \w will also match digits and '_'.    The regular expression is anchored at the beginning of the string in $checked so it will only match once so the use of the /g is also superfluous.    You are also capturing two strings which you aren't using so the capturing parentheses are also superfluous.    So, to sum up, you probably want something like:

       if ( $checked =~ /^[[:alpha:]]{3}\d{4,7}/ )
        {
          # it should print the accounts starting with letters here
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