In this revision (v3) I present four new successions, which are added to the previous four; in the image on page 6 of 11 I have compared the initial parts of the eight sequences. I also present the result of further verifications that I have performed; I decided to verify more than the others the b=b+b+b+1 sequence that I presented in the revision (v1) of this article. The checks concern the relationship that these different sequences have with prime numbers but also with composite numbers; I have also performed the same type of verifications for (2^a-2)/a (see Fermat's little theorem). As I have already described in the revision (v1) of this article and also in the previous one, I made four of the eight sequences starting from 2^a-2, 3^a-3, 4^a-4 and 5^a-5, the other four derive from a further elaboration.