Which predictive model is appropriate?

I’m completely lost when trying to choose the type of predictive model for my problem. Is it autoregressive model, nonlinear time series, Markov Chain or other? Can someone please give me some advise?

78,
18,
51,
89,
19,
43,
62,
28,
94,
49

Suppose, everyday I’m given 10 data, and an example was listed above. They’re random numbers generated by two devices, namely Device A and Device B. Each of them is capable to generate random numbers from 0 to 9.

The first number in the data is generated by Device A, while the second number is generated by Device B. For instance, for the first data of “78”, “7” was generated by Device A and “8” was generated by Device B. Similarly, for the last data of “49”, “4” was generated by Device A, and “9” was generated by Device B.

I want to be able to predict the next outcome variable after the last “49”.

I have a total of 300 historical data for 30 days.

From my initial investigation for the 300 data, every device tends to produce repeated sequences. For instance, Device A will repeat the sequence “6-2-9-4” (as in the last 4 data). That means this sequence appeared twice within the 300 historical data for Device A. For another example, the sequence “8-1-9-9” (the 2nd to the 5th data) in Device B appeared twice, too. Each of them produce at least three repeated sequences.

I’d like to predict the next outcome variable after the last “49”. Which model is more appropriate?

Thank you in advance!