Which predictive model is appropriate?
I will assume that by "random" you mean that the numbers don't follow any particular mathematical function. If they were really random then there wouldn't be any pattern to discover so there would be no point trying to predict anything.

From your description I understand the following:


The value of the digit doesn't have any numerical property. In particular the natural order doesn't play any role. This suggests that the digits can be considered as categorical variables.
The data is sequential (the order in the sequence of digits matters) but there is no notion of time involved.
Apparently the two devices produce two independent sequences. You might want to check but if this is the case this calls for two distinct models, one for each device (otherwise you should use a single joint model).


Based on these observations I would use a simple sequential model such as Hidden Markov Model or Conditional Random Fields.