These are my very first circuits, that I devised.
This one will shift a single lit LED in every clock pulse. It uses a HCF4017 Decade Counter, and NE555 in astable mode as a clock.
This one will produce a train of lit LEDs. It uses two NE555 in astable mode, on as a serial data input, and other as a clock, and a 74HC595 Shift Register.
The Train length sometimes is apparently random, because I didn’t fine tune the timing of the data input, and the shift clock.
I tested these circuits on breadboard, and it worked fine.