Abstract
We investigate the Fibonacci pseudoprimes of level k, and we disprove a statement concerning the relationship between the sets of different levels, and also discuss a counterpart of this result for the Lucas pseudoprimes of level k. We then use some recent arithmetic properties of the generalized Lucas, and generalized Pell–Lucas sequences, to define some new types of pseudoprimes of levels k+ and k− and parameter a. For these novel pseudoprime sequences we investigate some basic properties and calculate numerous associated integer sequences which we have added to the Online Encyclopedia of Integer Sequences.
Highlights
We define the generalized Lucas and Pell–Lucas pseudoprimality of level k, which involves the Jacobi symbol. For these notions we study some new related integer sequences indexed in the Online Encyclopedia of Integer Sequences (OEIS)
In [19] we proved connections between the sets of generalized Lucas and Pell–Lucas pseudoprimes of levels 1− and 2−, which are linked through the property n | Un2 − 1
In this paper we have analyzed the Fibonacci pseudoprimes of level k, and we have formulated an analogous version of this concept for the Lucas numbers (Section 2.2)
Summary
In our paper [7] we have defined a weak pseudoprimality notion for generalized Lucas sequences Un ( a, b). A composite integer n for which n | Un2 − 1 is called a weak generalized Lucas pseudoprime of parameters a and b This notion plays a key role in the present paper. For these notions we study some new related integer sequences indexed in the Online Encyclopedia of Integer Sequences (OEIS). Sometimes we have provided more terms than in the OEIS (which has a limit of 260 characters), so that the readers can check the numerical examples and counterexamples
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
