Below is the code

Sample data:
candseq data
SKA_HWI-EAS418:5:1:163:742#0/1
SKA_HWI-EAS418:5:1:30:1357#0/1
SKA_HWI-EAS418:5:1:53:520#0/1
SKA_HWI-EAS418:5:1:99:1255#0/1
SKA_HWI-EAS418:5:1:99:904#0/1

rawseq data
@SKA_HWI-EAS418:5:1:163:742#0/1
TGCTTCACAATGATAGGAAGAGCCGACATCGAAGGATTAAAAAGCGACGTCGCTATGAACGCTTGG
+SKA_HWI-EAS418:5:1:163:742#0/1
BBBBB@B?AAABA@A<?@<@?@<<?A?A@5>=<@=7??A>A;??;@@;;34?:<>=>7<??6>6:-
@SKA_HWI-EAS418:5:1:164:195#0/1
CGCAATACTGTATTGCCCTTAATGGGGTCACTGTAACATTTTAAAACAAATGAGCAGTGACTGACT
+SKA_HWI-EAS418:5:1:164:195#0/1
C+CCBCB@C?B>C?BABCCBBBCC30==:;CC<?+7C?BC>-3(=5.?:64=08@-AC;#######
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use 5.010.0;
use strict;
use warnings;


#Read in files

if ( @ARGV < 2 ){
        say "Please, type in 'perl task2.pl candseqfilename rawseqfile
+name' and hit enter";
        exit ;
}


open(CANDSEQ, "<", $ARGV[0]) or die "candseqfilename can't be read: pl
+ease check it: $!";

my ( @candseq, @rawseq, $rawseq );

while(<CANDSEQ>){
        chomp;
        push(@candseq, $_);
}

#print $_ for @candseq;

open(RAWSEQ, "<", $ARGV[1]) or die "rawseqfilename can't be read: plea
+se check it: $!";


while(<RAWSEQ>){
        chomp;
        $_ =~ s/^@// if/^@/;
        push(@rawseq, $_);
}

#say $_ for @rawseq;

for( my $count = 0; $count < @rawseq; $count += 4 ){

        for my $candseq( @candseq ){

                if(  $candseq ~~ @rawseq  ){
                        say "found match";
                }
        }
}
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If I understand you query correctly, a quick non perl solution is

grep -A2 -f candseq_data_file rawseq_data_file
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A perlish way of checking the presence of a string in an array is

@is_member = grep { $_ =~ /$candseq/} @rawseq;
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Your code worked for me though. It identified the first line of "rawseq data" as a match.

Note that in $candseq ~~ @rawseq, string equality is being checked. If you want SKA_HWI-EAS418:5:1:163:742#0/1 to match the second line "rawseq data" as well, try qr($candseq) ~~ @rawseq.

Reference: Section "Smart matching in detail" in perlsyn