A note on Perrin pseudoprimes
Steven Arno
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Source: Crossref
Published: Jan 1, 1991
DOI: 10.1090/s0025-5718-1991-1052083-9
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The cubic recurrence A ( n + 3 ) = A ( n ) + A ( n + 1 ) A(n + 3) = A(n) + A(n + 1) with initial conditions A ( 0 ) = 3 A(0) = 3 , A ( 1 ) = 0 A(1) = 0 , A ( 2 ) = 2 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 {10^{14}} .
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