LM317 - Input Voltage
The LM317 datasheet does not neglect to include the input voltage when calculating the resistors for the desired output voltage.

The input voltage is not needed.  The entire point of a voltage regulator is for the output voltage to be independent of the input voltage.

If the resistor values depended on the input voltage, then you would have to change the resistors every time the input changes.  That wouldn't be a very practical regulator.

If you are thinking of the common case of reducing a fixed, regulated voltage to a lower voltage, then I can see where the misunderstanding comes from.

But, linear regulators are intended to take a varying voltage and lower it to a fixed, stable voltage.  Linear regulators have an input range they can work in.

Your LM317 will provide a stable output voltage as long as the input voltage is below the maximum allowed (no more than 37V between input and output voltage) and the input is above the minimum (about 3V between input and output.)

So for an output voltage of 3V, you have a maximum input voltage of 40V and a minimum of 6V.  For any voltage in that range, the output will be fixed at 3V.  No resistor changes needed.



The above ignores overload conditions and the minimum load conditions.  Those are described in the datasheet.  If you have trouble with that, ask in a separate question.