If you add a resistor in series with each LED then you must increase the supply voltage.
The max allowed current in most ordinary LEDs is 30mA. I have some Luxeon SuperFlux LEDs with 4 pins that are rated at 70mA but at 50mA or more they get very hot.
If you have two 3.4V LEDs in series they need 6.8V and the LM317 current regulator needs an additional 3.25V so the minimum supply voltage will be 10.05v and will not work with only 6V.
The circuit shown can be wired in many ways since everything is in series.
The max allowed current in most ordinary LEDs is 30mA. I have some Luxeon SuperFlux LEDs with 4 pins that are rated at 70mA but at 50mA or more they get very hot.
If you have two 3.4V LEDs in series they need 6.8V and the LM317 current regulator needs an additional 3.25V so the minimum supply voltage will be 10.05v and will not work with only 6V.
The circuit shown can be wired in many ways since everything is in series.