Learning character sequences and predicting sequences
I think you might want to check Andrej Karpathy's work around charRNNs some pretty cool work is being done. The github link has all the relevant code too.
If you are looking for a more applied way - you can check my blog on deep learning gender from name which effectively uses character level LSTM RNNs to learn patterns : 
medium.com/@prdeepak.babu/deep-learning-gender-from-name-lstm-recurrent-neural-networks-448d64553044

Hope this help.