typeset -a hamming=(1) q2 q3 q5
function nextHamming {
    typeset -i h=${hamming[${#hamming[@]}-1]}
    q2+=( $(( h*2 )) )
    q3+=( $(( h*3 )) )
    q5+=( $(( h*5 )) )
    h=$( min3 ${q2[0]} ${q3[0]} ${q5[0]} )
    (( ${q2[0]} == h )) && ashift q2 >/dev/null
    (( ${q3[0]} == h )) && ashift q3 >/dev/null
    (( ${q5[0]} == h )) && ashift q5 >/dev/null
    hamming+=($h)
}

function ashift {
    typeset -n ary=$1
    printf '%s\n' "${ary[0]}"
    ary=( "${ary[@]:1}" )
}

function min3 {
    if (( $1 < $2 )); then
        (( $1 < $3 )) && printf '%s\n'$1 || printf '%s\n'$3
    else
        (( $2 < $3 )) && printf '%s\n'$2 || printf '%s\n'$3
    fi
}

for ((i=1; i<=20; i++)); do
    nextHamming
    printf '%d\t%d\n' "$i" "${hamming[i-1]}"
done
for ((; i<=1690; i++)); do nextHamming; done
nextHamming
printf '%d\t%d\n' "$i" "${hamming[i-1]}"
printf 'elapsed: %s\n' "$SECONDS"