Sequences of degree distribution for low-density erasure codes are investigated.We propose a necessary and sufficient condition for sequences of degree distribution for low-density erasure codes to be capacity-achieving sequences.The properties of the Heavy-Tail/Poisson sequences and right-regular sequences are given for low-density erasure codes.The analytical property of capacity-achieving sequences is shown for low-density erasure codes.These analytical properties of the sequences of degree distribution will be helpful in designing capacity-achieving sequences of degree distribution for low-density erasure codes.