7 segment display with given sequence
You can have two different machine states produce the same output, there's no need to use the same state to represent the repeated digits.
call your machine states s1 s2 s3 s4 etc. they have a simple progression where each changes to the next state on a clock signal. you need 8 one for each place in your output (or more depending on what happens after the last digit.)
Now draw a Karnaugh map for each segment of the 7 segment vs the flip-flops or counters you used to make the states.