The protein sequence is coded with the help of the triplets of nucleotides, each corresponding to one amino acid in a protein sequence. The triplet code of the coding sequences possesses some informative redundancy. Some triplets are more probable than others. The analogous redundancies appear in all natural languages. The non-equal frequency of the characters in plain text makes possible that entire words can be predicted given the context of the plain text. This is typical problem in cryptanalysis that a plain text is compressed before encrypting it in order to reduce the language redundancies. The nucleotides represent the natural units to discuss the redundancies in the coding sequences of natural genomes. The mutation pressure and selection pressure are the main factors responsible for the observed redundancies. Then, the nucleotide frequency in DNA seems to be the natural information weight. We show, that the probability of a nucleotide to stay nonmutated becomes another, the more efficient information weight. It has smaller redundancy although it is correlated with the nucleotide frequency. We have found the values of probability for nucleotide to stay non-mutated in the particular case of the Borrellia burgdorferi genome. In order to examine the usefulness of the new frequencies we used them in a problem of bit-string packing in a channel with a given capacity. We performed a computer experiment, in which we have generated all possible oligomers consisting of k nucleotides and we have shown, that if the number of bits of the information carried out by the oligomers does not exceed a given threshold value, the same as calculated for genes of the Borrelia burgdorferi genome, then the distribution of the generated oligomers resembles the one used by these genes.