Move the file open and close outside the print loop. Note too that you should always check open results, use lexical file handles and use the three parameter version of open:

open my $out, '>', $fileName or die "Can't open '$fileName': $!\n"
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That is because you overwrite the file each time you open it. Try appending instead:

open OUT, ">>results5";
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Also, consider checking the results from open and responding accordingly to errors:

open OUT, ">>results5" or die "Cannot write to output: $!\n";
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L-LL-L--L-LL-L--L-LL-L--
-R--R-RR-R--R-RR-R--R-RR
B--B--B--B--B--B--B--B--
H---H---H---H---H---H---
(the triplet paradiddle with high-hat)

from what code you have posted

{
    print "pos $i $testseq\n";
    open OUT, ">results5";
    print OUT "pos $i $testseq\n";
    close OUT;
    
}
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You have print statements which print to your screen but when you open the file and print to the file using print filehandle i.e. print OUT ..It prints to the file..So only the last print stmt shows up in the file .You can open this file at the beginning of the loop and change all print statements to print filehandle i.e. print OUT

as an alternative you can redirect the stdout of your script by redirecting it to a file like below (so that it will write all print statements to your log file)

perl script1.perl >> script1.log 
#redirect stderror Also as below 
perl script1.perl >> script1.log 2>&1
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Thanks! You guys are the best! Really appreciated the extra tips, too.