This study addresses several important questions related to naturally underrepresented sequences: (i) are there permutations of real genomic DNA sequences in a defined length (k-mer) and a given lineage that do not actually exist or underrepresented? (ii) If there are such sequences, what are their characteristics in terms of k-mer length and base composition? (iii) Are they related to CpG or TpA underrepresentation known for human sequences? We propose that the answers to these questions are of great significance for the study of sequence-associated regulatory mechanisms, such cytosine methylation and chromosomal structures in physiological or pathological conditions such as cancer.