Perfect for a shell script: I used bash.

bash
for i in *
do
   (echo $i; cat $i; echo ) > tmp
   mv tmp $i
done
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I'm preseuming newline was supposed to indicate an empty line.

--
TTTATCGGTCGTTATATAGATGTTTGCA

perl -pi -e '$_=">$ARGV\n$_\n"' *.txt
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while(<>){}
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Update: I read the question better & turned down the flame-o-meter on this comment...

This code might get you in trouble if there are newlines in the file. If that is the case then...

It puts "filename.txt" as every other line in the file. The while loop is what gets you in trouble here. Perhaps if you do a undef $/ somewhere in there.

Or, even better, start with your version and test for the first line.

perl -pi -e '$ARGV =~ s/\.txt//; $_=">$ARGV\n$_\n if($.==1)"' *.txt
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This adds three things - it removes the .txt from the filename first. Second, it adds the initial '>' character. Finally, it only rewrites the first line. ($. is line number).

Not the most elegant, but it works.

Umm, I said "If each file really is "straight text, no carriage returns, no spaces, etc. " If there are no carriage returns there is only one line. If you are getting the file name every other line than your file has one more than one line and doesn't fit the requirement straight text, no carriage returns, no spaces, etc. Also, no where is it specified to remove the ".txt". In fact the example specifically shows the ".txt" being there

filename: a36.txt
initial filecontents :

AATGACGTACGTAGTCGTAGCGT

after script filecontents :

>a36.txt
AATGACGTACGTAGTCGTAGCGT
[newline]
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#!perl

use strict;
use warnings;

use Tie::File;

my $dir = q[path/to/dir];

opendir(DIR, $dir) or die "Could not open '$dir': $!\n";
my @files = grep { -T and /a\d+\.txt/ } readdir(DIR);
close DIR;

for my $file (@files) {
   my @lines;
   tie @lines, 'Tie::File', "$dir/$file" or die "Failed tieing '$file'
+: $!\n";
   unshift @lines, $file;
   untie @lines;
}
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I'll second that. If you're doing any sort of biologic sequence manipulation, you must have bioperl.

Here's some incentive to get it installed... Run this with an argument of '*.txt'.

use Bio::Seq;
use Bio::SeqIO;

while(my $fname = shift) {
  open(INSEQ, "<$fname") or die $!;
  my $seq;
  ## Grab all the sequence in a single string
  while(<INSEQ>) {
      chomp;
      $seq .= $_;
  }
  close INSEQ;
  my $fname =~ s{\.txt}{}; # strip .txt

  ## Create a new Bio::Seq object with your sequence
  my $seqobj = Bio::Seq->new(-display_id => $fname,
                             -seq  => $seq
                             );

  ## Write it out to filename.fa
  my $outfile = $fname . ".fa";
  my $seqout = Bio::SeqIO->new(-format => 'fasta',
                               -file   => "> $outfile",
                               );
  $seqout->write_seq($seqobj);
}
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It'll do exactly what you asked. Plus, just change 'fasta' to some other format, and it will convert that too.

Well, I didn't realize your input files were all newline free.. Should have read the question more closely.

In that case, Bioperl is even better...

use Bio::SeqIO;
while (my $fname = shift) {
   ## raw is one seq per line (no newlines)
   my $in  = Bio::SeqIO->new(-file => "$fname",
                            '-format' => 'raw');
   $fname =~ s{\.txt}{}' # strip .txt
   my $outfile = $fname . ".fa";
   my $out = Bio::SeqIO->new(-file => "> $outfile" ,
                           '-format' => 'fasta');
 
   ## Do the conversion
   while ( my $seq = $in->next_seq() ) {
       $seq->display_id($fname); # Add a name
       $out->write_seq($seq);
   }
}
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Run it in the same way, with an argument of *.txt

#!/usr/bin/perl
use warnings;
use strict;

# open current dir, and read in all files
#   matching /^a\d+\.txt/ into the array @files:
#
opendir my $dir_handle, "." or die "can't open dir";
my @files = grep { /^a\d+\.txt/ } readdir $dir_handle;
closedir $dir_handle;

# For each of the files:
#
foreach my $filename ( @files ) {
    # open the file, and read its contents into the
    #    array @file_contents, then close the file:
    #
    open my $fh, "$filename" or die "can't open $filename to read";
    my @file_contents = <$fh>;
    close $fh;

    # now reopen the file (for writing), and write your
    #    desired output to it:
    #
    open $fh, ">$filename" or die "can't open $filename to write";
    print $fh ">$filename\n@file_contents\n";
    close $fh;
}
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No one has recommended the append mode of open. Here is the perl one-liner:

perl -e 'for (@ARGV){open FILE, ">>$_";print FILE "\n";close FILE;} ' 
+<filenames>
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Later

Your code doesn't do what is asked. That one liner will append a newline to the end of the file.