Use Biopieces www.biopieces.org) and try something like this:

read_fastq -i file1.fq,file2.fq | patscan_seq -i -c -p acgtactagctagctactagc[2,1,1] | grab -p PATTERN -K | write_fastq -o matched.fq -x

This allows for 2 mismatches, 1 insertion and 1 deletion (and ambiguity codes).

gunzip and paste both fasts on the fly, with awk , group by '4 lines', test if the pair matches your needs (here first read starts with the regex "^ATGGG[GC]AAAA*" split the output into two files using awk.

paste <(gunzip -c input_1.fastq.gz) <(gunzip -c input_2.fastq.gz)  |\
awk '{a[i]=$0;++i;if(i==4){split(a[1],S,"\t"); if(S[1] ~ "^ATGGG[GC]AAAA*") {for(j=0;j<4;++j) printf("%s\n",a[j]);}; i=0;}}' |\
awk -F '    ' '{print $1 >> "select_1.fq"; print $2 >> "select_2.fq";}'

You can try meme:

http://meme.nbcr.net/meme/cgi-bin/meme.cgi

Although if you are using raw reads, you'll probably have quite a large signal-to-noise ratio. It might be a better idea to align them first and then use the regions that they align to as inputs to a motif finding program.

Well, MEME might not be the right choice for this, but FIMO could be used... It allows motif discovery based on PWM .