Products of Fermat or Mersenne numbers in some sequences.

Let Pn be an n-th Padovan number, En an n-th Perrin number, and Nn an n-th Narayana number. In this paper, we solve the Diophantine equations Pn = (2a - 1)(2b -1), En = (2a - 1)(2b - 1), and Nn = (2a ± 1)(2b ± 1), in positive integers n, a and b. Therefore, we determine the Padovan or Perrin numbers that are products of two Mersenne numbers and the Narayana numbers that are products of two Mersenne or Fermat numbers. [ABSTRACT FROM AUTHOR]