The frequencies of occurrence of the 5’ and 3’nearest neighbor doublets of oligonucleotides containing (G/C) and (A/T) blocks show strong trends. Specifically, the following trends are observed. Given a (G/C)n (A/T)m oligomer (where G/C)n indicates a sequence of length n composed solely of Gs and/or Cs and (A/T) is a sequence of length m composed solely of As and/or Ts, and n=3, 2, 1; m= 1, 2, 3) and a (G/C)2 doublet, (G/C) (A/T)m(G/C)2 > (G/C)n+2(A/T)m. That is the (G/C)2 doublet is preferentially located 3’ of the oligomer, enclosing the (A/T)m stretch. The trends are strongest for n=3, m = 1 and gradually weaken as the size of the (G/C)n block decreases (with a concomitant increase of (A/T)). (A/T)2 nearest neighbor flank preferentially encloses the (G/C)n block (to produce (A/T)2 (G/C)n (A/T)m). The (A/T)2 flank trends are weaker than the (G/C)2 flank ones. The (A/T) flank trends also decrease in strength as the size of the (G/C)n block decreases. The statistical significance of these trends in eukaryotes is very high. A possible correlation with DNA structural parameters, in particular groove geometry, is discussed.