This is what I did, it should work:
#!/bin/bash
DATE=$1
REGEX="^(..)(..?)(.)$"
[[ $DATE =~ $REGEX ]]
YEAR=$(( ${BASH_REMATCH[1]} + 1999 ))
WEEK=$(( ${BASH_REMATCH[2]} - 1))
DAYOFWEEK=$(( ${BASH_REMATCH[3]} - 1))
OFFSET=$(( 6 - $(date -d "$YEAR-07-01" +%u) ))
DATEOFFIRSTSATURDAY=$(date -d "$YEAR-7-01 $OFFSET days" +%d)
FINALDATE=`date -d "$YEAR-07-$DATEOFFIRSTSATURDAY $WEEK weeks $DAYOFWEEK days"`
echo $FINALDATE
It worked for the two dates given above… If you want to customize the date output, add a format string at the end of the FINALDATe assignment.
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