You've been given excellent suggestions (!):

• choroba shows the three-argument open, including using lexically-scoped variables (don't use global variables for file opens).
• 2teez shows a crucial first step: always use strict; use warnings;
• pvaldes imparted a hint on counting the number of "F"s in the sequence

Not to confuse matters here, but for your future reference (since you appear to be on a bioinformatics path), consider becoming well acquainted with Bio::SeqIO and its set of related modules.

Just as there are well-developed modules to parse HTML, XML, and CSV files, Bio::SeqIO lives to do the same for Fasta and other such formats.

For example, to retrieve and process each sequence within a Fasta file, you can do the following:

use strict;
use warnings;
use Bio::SeqIO;

print "Please type the file name of the protein sequence data: ";
chomp( my $proteinfilename = <STDIN> );
print "\n";

my $fastaIN = Bio::SeqIO->new( -file => $proteinfilename, -format => '
+Fasta' );

while ( my $seq = $fastaIN->next_seq() ) {
    print $seq->seq, "\n";
}
[download]

Each sequence in the Fasta file is accessible using the $seq->seq notation. The first part before the arrow operator is the sequence object; the part after the arrow operator is the method. These methods are covered in detail in the Bio::Seq module's documentation. In the example above, the sequence is printed, but a character count could be done there, too.

Hope this helps!