I want to build a 4 LED circuit where the LED's light up 1,2,3,4 but each one stays lit until #4 then it starts over. Will this circuit do it?
Welcome to Bittech! My electronics aren't up to par, so I can't provide any real help. (but I can bump your topic for the more electronic minded!) I was thinking some combo of 555 timer and appropriately size caps could do it. I'm not sure what a 4015 is but it looks like you've got some good thinking going on. What'd you use to create the diagram?
Looks fine to me, should work. although the 4015 might not be able to drive the LEDs cannot remember how much the outputs can source. You will prob have to drive the LEDs with transistors see http://www.doctronics.co.uk/4015.htm