Wow, this really got complicated. Your original 30 LED chain needs 4.5 volts to operate. Assuming they are wired in parallel, which they seem to have to be, you would need 1/10 the voltage to power 3 LEDs, or 1/2 volt, roughly. So, you would need a resistor to drop a 1.5 volt battery voltage down to .5 volts. Assume the current needed is ??. The resistor needs to be 1/?? ohms. This isn't critical because an AA battery voltage would droop considerably with the amount of current you need. Unfortunately I don't know how much current those LEDs need. I think I would look for a trim pot to put in the circuit and use it as a rheostat to adjust the current up from zero to where the LEDs light up.
EDIT: I'm confused! You need 1/10 the current to power 3 LEDs, not voltage. But, you still need the same voltage, or 4.5 volts. So, you need to determine the forward voltage drop across one LED, and the desired current in order to figure out what size resistor is needed. But, it used a 10 ohm resistor for 30X one LED's current, to drop the voltage down to equal the forward voltage drop. So, perhaps (?) you need 100 ohm to get the same voltage drop when using only 3 LEDs (1/10 the current)
Last edited by Hoppy; 01-05-2012 at 04:38 PM.