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A013998
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Unrestricted Perrin pseudoprimes.
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4
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271441, 904631, 16532714, 24658561, 27422714, 27664033, 46672291, 102690901, 130944133, 196075949, 214038533, 517697641, 545670533, 801123451, 855073301, 903136901, 970355431
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| "The column Mathematical Recreations by Ian Stewart in the June 1996 issue of Scientific American discusses the Perrin sequence [A001608] A(n) defined by A(0)=3, A(1)=0, A(2)=2, A(n+1)=A(n-1)+A(n-2). Motivated by a theorem of E. Lucas: If n is prime it divides A(n) exactly, the question whether primality of n follows from n divides A(n) exactly was formulated 1899. So far, they say, nobody has found a composite n that divides A(n). Such a number would be called a Perrin pseudoprime. The article quotes an experiment by Steven Arno of the Supercomputing Research Center in Bowie, Md., where a lower bound of 15 digits for the size of the smallest Perrin pseudoprime was obtained in 1991. On Jul 3rd, 1996, I was able to find the two smallest Perrin pseudoprimes:" - Holzbaur
In the "Feedback" section of his column for November 1996, Ian Stewart mentions that Jeffrey Shallit (Waterloo) had written to him saying that he had found the Perrin pseudoprimes 271441 and 904631 in 1982.
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REFERENCES
| W. W. Adams and D. Shanks, Strong primality tests that are not sufficient, Math. Comp. 39 (1982), 255-300.
Ian Stewart, Tales of a neglected number, Scientific American, No. 6, 1966, pp. 92-93.
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LINKS
| Christian Holzbaur, Perrin pseudoprimes, [broken link, see U Vienna personnel ]
Ian Stewart, "Tales of a Neglected Number"
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to pseudoprimes
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CROSSREFS
| Cf. A018187.
Sequence in context: A075467 A206001 A137715 * A114663 A151650 A128479
Adjacent sequences: A013995 A013996 A013997 * A013999 A014000 A014001
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KEYWORD
| nonn,more
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AUTHOR
| R. K. Guy (rkg(AT)cpsc.ucalgary.ca)
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EXTENSIONS
| More terms from alipson(AT)cix.compulink.co.uk (Andrew Lipson). Further terms beyond those shown here have been computed by cdw10(AT)cix.compulink.co.uk (C Wright).
Holzbaur quote from Robert G. Wilson, Nov 30, 2001
Marked broken link - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 09 2010
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