AbstractEach gene population F (i.e. a set of DNA sequences) can be considered as a language F on the two letter alphabet {R,Y) (R=purine: adenine or guanine; Y=pyrimidine: cytosine or thymine) issued from the EMBL gene database (release 21). For each language F, an autocorrelation function p is defined associating to each i in the range 11,99] the probability pi(F) of occurrence of the two same factors YRY separated by i letters over all words in F. The associated curve C(F): i->pi(F) reveals in the first part two properries naturally associated with the biological features of the gene population F:- Property 1: a periodicity P3 (modulo 3 periodicity) associated with the maximal value pg(F) if F is a protein coding gene population.- Property 2: a periodicity P2 (modulo 2 periodicity) associated with the maximal value p3(F) if F is a noncoding gene population.In the second part, we, prove that:(1) The rational language (YRY(N)g)* (where (N)g is any word of length 6) associated with random insertions and deletions of factors of three letters leads to rite property 1.(2) The rational language (YRY(N)3)* (where (N)3 is any word of length 3) associated with random insertions and deletions of single letter leads to the property 2.Therefore, the two types of words YRY(N)g and YRY(N)3 constitute small primitive DNA strings which may have a central function in DNA sequence evolution.