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Mathematics of Computation

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A note on Perrin pseudoprimes


Author: Steven Arno
Journal: Math. Comp. 56 (1991), 371-376
MSC: Primary 11A41; Secondary 11Y16
DOI: https://doi.org/10.1090/S0025-5718-1991-1052083-9
MathSciNet review: 1052083
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Abstract: The cubic recurrence $ A(n + 3) = A(n) + A(n + 1)$ with initial conditions $ A(0) = 3$, $ A(1) = 0$, $ A(2) = 2$, known as Perrin's sequence, is associated with several types of pseudoprimes. In this paper we will explore a question of Adams and Shanks concerning the existence of the so-called Q and I Perrin pseudoprimes, and develop an algorithm to search for all such pseudoprimes below some specified limit. As an example, we show that none exist below $ {10^{14}}$.


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DOI: https://doi.org/10.1090/S0025-5718-1991-1052083-9
Article copyright: © Copyright 1991 American Mathematical Society