Hi Ed,
OK, yours will work, BUT you have to sink 300mA to do it! If you put the resistor in, then you only need to sink 1.25V/1k + the adj pin current, max 100uA. With the 1k in there, the LED string sees 1.25V plus Vce(sat), say 1.35V, but so what? Even red LEDs have negligible current when hot at 0.5 volts each. Much less power hungry to add the
1k in there. The 1k is nominal, of course; it could be 220 ohms, or 2.2k ohms, though with 2.2k, I'd start worrying about the voltage drop across the 2.2k when the LEDs light; that increases the drop across the 4 ohm resistor by about 0.1 volts. 1k seemed a reasonable compromise to get to low current in the "yank down control transistor." Revised version, as I had posted, below. Thanks for providing the framework to edit!Cheers, Tom