We prove that the number of fractions h 1 / h 2 of integers h 1 , h 2 a subset A ⊂ H∩[1, X ] is at least α X/(log X) 3/2 , where H is the set p −1, p being a prime such that p +1 is a sum of two coprime squares. So, this number of fractions is ε α 1+ε |A| 2 , where ε is any positive real number. We take this opportunity to describe a geometrical view of the sieve and its usage to study integer sequences.