login
This site is supported by donations to The OEIS Foundation.

 

Logo

Invitation: celebrating 50 years of OEIS, 250000 sequences, and Sloane's 75th, there will be a conference at DIMACS, Rutgers, Oct 9-10 2014.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

When these pseudoprimes are subjected to a Fermat based primality test (b^(a(n)-1) mod a(n) = 1), only a(2) = 2465 passes for b = 2 or 3 and only 68251 passes for b = 5. - Gary Detlefs, Feb 26 2013

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

CROSSREFS

Sequence in context: A091553 A224491 A126830 * A183795 A074869 A212476

Adjacent sequences:  A005842 A005843 A005844 * A005846 A005847 A005848

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from David Broadhurst.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified August 29 04:10 EDT 2014. Contains 246185 sequences.