A generalization of Piatetski-Shapiro sequences (II)

Suppose that alpha, beta is an element of R. Let alpha >= 1 and c be a real number in the range 1 < c < 12/11. In this paper, it is proved that there exist infinitely many primes in the generalized Piatetski--Shapiro sequence, which is defined by ([alpha n(c)+ beta])(n=1)(infinity). Moreover, we also prove that there exist infinitely many Carmichael numbers composed entirely of primes from the generalized Piatetski--Shapiro sequences with c is an element of(1,(19137)/(18746)). The two theorems constitute improvements upon previous results by Guo and Qi [5].