/diy/ - Do It Yourself

completely new to this, but I was playing with this circuit and changing different values of resistors for the R2 resistor to see when the led would turn on.
when I inserted a 47 ohm resistor for R2 the led stayed off, but when I inserted a 100 ohm one it turned on. The led is a blue led rated at 3-3.3v 20mA.

what would be the way to mathematically select the right resistor value for the blue led to turn on?

and does the led have a voltage drop or resistance? is the NPN transistor a load? why am I only seeing 1 mA of current flow to the led even though my bench supply is maxing out the current limit of 20mA?