Identifying repeating sequences of data in byte array
I believe the problem that you are referring to, is that of "Motif Discovery in Time Series Data". An appreciable amount of research literature already exists in this domain, so you can look through those. If the data that you handle is not very large, you can find some relatively easy to implement algorithms. 

If the data is large , you can look at more recent publications in this domain. As a starting point I would recommend taking a look at how Motif Discovery is done in SAX. SAX takes continuous signals as inputs and discretizes them. These discrete levels are then stored as alphabets. This resulting data looks very much like yours in my opinion. Take a look at what they do in "Mining Motifs in Massive Time Series Databases".