Penlights are typically double AAA.
The most frequently recommended is the preon.
You mentioned cheap.
I have two CQG S2 2AAA penlights. One in Neutral white, the other cool white. I prefer the neutral, but I don't see it offered anywhere anymore. cnqualitygoods has it for less than $20
Make sure that you also pick up the pocket clip for it.
It is smooth, stainless steel, and high, low and strobe, without memory.