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.

中文翻译：

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关于k级的广义卢卡斯伪素性

我们研究了k级的Fibonacci伪素数，我们不赞成关于不同水平的集合之间的关系的陈述，并且还讨论了k级的Lucas伪素数的这一结果的对应物。然后，我们使用广义Lucas以及广义Pell–Lucas序列的一些最新算术性质，来定义一些新的水平伪素数类型${ķ}^{+}$ 和 ${ķ}^{-}$和参数a。对于这些新颖的伪素数序列，我们研究了一些基本属性并计算了许多相关的整数序列，这些整数序列已添加到在线整数序列百科全书中。