You want to select the resistance based on what the datasheet of your exact component tells you. There are so many different LM317 manufacturers that their implementation will vary, and you can select the resistance that fits for all LM317 type regulators.
LM317 type regulators must have a minimum load current to keep their output well regulated. This current is stated in the datasheets. But if it is 5mA, then R1 should be 240 ohms in most datasheets. Some datasheets say 10mA, so R1 would be 120 ohms.
Since you used 10k resistor, it does not draw enough load current, and the regulator output voltage is not what you expect.
And you seem to want 3.7V; I hope you are not using it to charge lithium batteries.