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A005845
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Bruckman-Lucas pseudoprimes: n | (L_n - 1), where n is composite and L_n = Lucas numbers A000032.
(Formerly M5469)
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22
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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
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OFFSET
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1,1
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COMMENTS
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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 and a Fermat pseudoprime to the first 407 prime bases. - Dana Jacobsen, Jan 10 2015
n in A002808 such that A213060(n) = 1. - Robert Israel, Jul 14 2015
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REFERENCES
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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).
Somer, Lawrence. "Generalization of a Theorem of Bruckman on Dickson Pseudoprimes." Fibonacci Quarterly 60:4 (2022), 357-361.
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..10000 (from Dana Jacobsen's site, terms 1..1000 from T. D. Noe)
Dorin Andrica and Ovidiu Bagdasar, Recurrent Sequences: Key Results, Applications, and Problems, Springer (2020), p. 88.
Dorin Andrica and Ovidiu Bagdasar, On Generalized Lucas Pseudoprimality of Level k, Mathematics (2021) Vol. 9, 838.
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.
Dana Jacobsen, Pseudoprime Statistics, Tables, and Data.
Eric Weisstein's World of Mathematics, Lucas Pseudoprime.
Index entries for sequences related to pseudoprimes
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MAPLE
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with(combinat):lucas:=n->fibonacci(n-1)+fibonacci(n+1):
test:=n->lucas(n) mod n=1:select(test and not isprime, [seq(n, n=1..10000)]); # Robert FERREOL, Jul 14 2015
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MATHEMATICA
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Select[Range[2, 170000], !PrimeQ[#]&&Divisible[LucasL[#]-1, #]&] (* Harvey P. Dale, Mar 08 2014 *)
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PROG
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(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
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CROSSREFS
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Cf. A000032, A002808.
Cf. A094394, A094395 (analogous numbers with the Fibonacci sequence). - Robert FERREOL, Jul 14 2015
Cf. A213060 (L(n) mod n).
Sequence in context: A091553 A224491 A126830 * A183795 A335092 A252692
Adjacent sequences: A005842 A005843 A005844 * A005846 A005847 A005848
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KEYWORD
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nonn,nice,changed
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from David Broadhurst
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STATUS
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approved
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