Bash rename with logical-mathematical operations

Question

I have files with the following naming-logic .JPEG (old cameras). e.i., DSC01415.JPEG.

My riddle has been that I would like to make something like:

mv DSC{1415..4131}.JPEG DSC{0001..3517}.JPEG

Which has equal effect of, for any file:

mv DSC<number>.JPEG DSC<number-less-1414>.JPEG

Answer 1

Would you please try the following:

for ((i = 1415; i <= 4131; i++)); do
    oldname=$(printf "DSC%04d.JPEG" "$i")
    newname=$(printf "DSC%04d.JPEG" "$((i - 1414))")
    if [[ -f $oldname && ! -f $newname ]]; then
        echo mv -- "$oldname" "$newname"
    fi
done

If the output looks good, drop the echo.
Please make sure to create the backup before execution not to lose your precious pictures by accident.