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
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.
Dana Jacobsen, Pseudoprime Statistics, Tables, and Data.
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
(Python)
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
L0, L1 = 2, 1
for k in count(1):
L0, L1 = L1, L0+L1
if k > 1 and not isprime(k) and (L0-1)%k == 0:
yield k
print(list(islice(agen(), 32))) # Michael S. Branicky, Apr 07 2024
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from David Broadhurst
STATUS
approved