A note on Perrin pseudoprimes
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- by Steven Arno PDF
- Math. Comp. 56 (1991), 371-376 Request permission
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 ${10^{14}}$.References
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- William W. Adams, Characterizing pseudoprimes for third-order linear recurrences, Math. Comp. 48 (1987), no. 177, 1–15. MR 866094, DOI 10.1090/S0025-5718-1987-0866094-6
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Additional Information
- © Copyright 1991 American Mathematical Society
- 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