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A005845 Bruckman-Lucas pseudoprimes: n | (L_n - 1), where n is composite and L_n = Lucas numbers A000032.
(Formerly M5469)
22
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 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
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).
Somer, Lawrence. "Generalization of a Theorem of Bruckman on Dickson Pseudoprimes." Fibonacci Quarterly 60:4 (2022), 357-361.
LINKS
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.
Eric Weisstein's World of Mathematics, Lucas Pseudoprime.
MAPLE
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
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. 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
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from David Broadhurst
STATUS
approved

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Last modified March 19 01:34 EDT 2024. Contains 370952 sequences. (Running on oeis4.)