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A005845 Lucas pseudoprimes: n | (L_n - 1), where n is composite and L_n = Lucas numbers A000032.
(Formerly M5469)
12
705, 2465, 2737, 3745, 4181, 5777, 6721, 10877, 13201, 15251, 24465, 29281, 34561, 35785, 51841, 54705, 64079, 64681, 67861, 68251, 75077, 80189, 90061, 96049, 97921, 100065, 100127, 105281, 113573, 118441, 146611, 161027 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This uses the definition of "Lucas pseudoprime" by Bruckman, not the one by Baillie and Wagstaff. - R. J. Mathar, Jul 15 2012

Unlike the earlier Baillie-Wagstaff Lucas pseudoprimes A217120, these have significant overlap with the Fermat primality test.  For example, the number 82380774001 is both an A005845 Lucas pseudoprime as well as a Fermat pseudoprime to the first 407 prime bases. - Dana Jacobsen, Jan 10 2015

REFERENCES

P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 104.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

R. Baillie and S. S. Wagstaff,Lucas pseudoprimes, Math. Comp 35 (1980) 1391-1417

P. S. Bruckman, Lucas Pseudoprimes are odd, Fib. Quart. 32 (1994), 155-157.

Eric Weisstein's World of Mathematics, Lucas Pseudoprime.

Index entries for sequences related to pseudoprimes

MATHEMATICA

Select[Range[2, 170000], !PrimeQ[#]&&Divisible[LucasL[#]-1, #]&] (* Harvey P. Dale, Mar 08 2014 *)

PROG

(PARI) is(n)=my(M=Mod([1, 1; 1, 0], n)^n); M[1, 1]+M[2, 2]==1&&!isprime(n)&&n>1 \\ Charles R Greathouse IV, Dec 27 2013

(Haskell)

a005845 n = a005845_list !! (n-1)

a005845_list = filter (\x -> (a000032 x - 1) `mod` x == 0) a002808_list

-- Reinhard Zumkeller, Nov 13 2014

CROSSREFS

Cf. A000032, A002808.

Sequence in context: A091553 A224491 A126830 * A183795 A252692 A074869

Adjacent sequences:  A005842 A005843 A005844 * A005846 A005847 A005848

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from David Broadhurst.

STATUS

approved

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Last modified May 27 01:17 EDT 2015. Contains 257849 sequences.