  DNA sequences are fundamental for encoding genetic information. The genetic
information may not only be understood by symbolic sequences but also from the
hidden signals inside the sequences. The symbolic sequences need to be
transformed into numerical sequences so the hidden signals can be revealed by
signal processing techniques. All current transformation methods encode DNA
sequences into numerical values of the same length. These representations have
limitations in the applications of genomic signal compression, encryption, and
steganography. We propose an integer chaos game representation (iCGR) of DNA
sequences and a lossless encoding method DNA sequences by the iCGR. In the iCGR
method, a DNA sequence is represented by the iterated function of the
nucleotides and their positions in the sequence. Then the DNA sequence can be
uniquely encoded and recovered using three integers from iCGR. One integer is
the sequence length and the other two integers represent the accumulated
distributions of nucleotides in the sequence. The integer encoding scheme can
compress a DNA sequence by 2 bits per nucleotide. The integer representation of
DNA sequences provides a prospective tool for sequence compression, encryption,
and steganography. The Python programs in this study are freely available to
the public at https://github.com/cyinbox/iCGR
