--- That won't work because if you use "4" to both reset the counter and pull the serial input of the shift register high, "4" will go low as soon as the counter is reset and there won't be anything to clock into the shift register when the next 555 clock comes along. :-(
What _will_ work is if you connect the counter's "0" output to the shift register's serial input and reset the counter with one of the other counter outputs.
For instance, if you wanted to have every 4th LED lit, you'd connect "0" to the shift register's input and "3" to the counter's RESET pin.
Want every third one lit? Connect "2" to RESET, and so forth.
Here's the timing for every fifth LED lit. (3 unlit LEDs between the lit ones. View in Courier)
_ _ _ _ _ _ _ _ _ _ _ _ CLK _| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| | ___ ___ ___ "0" _| |___________| |___________| |_________ ___ ___ ___ "1" _____| |___________| |___________| |_____ ___ ___ ___ "2" _________| |___________| |___________| |_ ___ ___ _ "3" _____________| |___________| |___________|
"4" _________________|_______________|_____________
_ _ _ _ _ _ _ _ _ _ _ _ CLK _| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| | ___ ___ ___ SIN _| |___________| |___________| |_________ ___ ___ ___ QA_______| |___________| A |___________| A |_____ ___ ___ ___ QB___________| |___________| B |___________| |_ ___ ___ _ QC_______________| |___________| |___________| ___ ___ QD___________________| |___________| |_________ ___ ___ QE_______________________| E |___________| E |_____ ___ ___ QF___________________________| F |___________| |_
CLK is the 555 clock; I've just shown it twice to make it easier to see the timing.
--- JF