Primes in a Sparse Sequence Original Research Article

In this paper, we consider the sequence 11, + 11 + 22, 11 + 22 + 33, … and prove some of its congruence properties. Surprisingly, this sequence is uniformly distributed in the residue classes (mod m) where m not identical with 0 (mod 4). Using these results and Selberg′s sieve, we obtain an upper hound for the number of primes in the sequence which are ≤ x.