1,1

"The column Mathematical Recreations by Ian Stewart in the Jun issue of Scientific American discusses the Perrin sequence [A001608] A(n) with: 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

W. W. Adams and D. Shanks, Strong primality tests that are not sufficient, Math. Comp. 39 (1982), 255-300.

Christian Holzbaur, Perrin pseudoprimes

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for sequences related to pseudoprimes

Cf. A018187.

Sequence in context: A139028 A075467 A137715 this_sequence A114663 A151650 A128479

Adjacent sequences: A013995 A013996 A013997 this_sequence A013999 A014000 A014001

nonn,more

R. K. Guy (rkg(AT)cpsc.ucalgary.ca)

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 rgwv, Nov 30, 2001