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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
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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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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
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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