Measured amperage differs greatly from my math
The resistance is calculated from the voltage across the resistors, which is the battery voltage minus the LED voltage (your schematic shows the LED backwards, but obviously that's not what you've built). 

Using your original numbers (4.8V-3.1V)/0.02A = 85\$\Omega\$

Using your measured battery voltage: (5.17-3.1)/0.02 = 103

So try 100\$\Omega\$.