On the recurrence ((((P*2-d)*2-d)*2-d)...) on Poulet numbers P having a prime factor d

In this paper I note two sequences of Poulet numbers: the terms of the first sequence are the Poulet numbers which can be written as P*2 – d; the terms of the second sequence are the Poulet numbers which can be written as (P*2 – d)*2 - d, where P is another Poulet number and d one of the prime factors of P. I also conjecture that the both sequences are infinite and I observe that the recurrent relation ((((P*2 – d)*2 – d)*2 – d)...) conducts sometimes to more than one Poulet number (for instance, starting with P = 4369 and d = 257, the first, the second and the third numbers obtained are 8481, 16705 and 33153, all three Poulet numbers).