OFFSET
1,1
COMMENTS
Composite n such that Q^(n-1) = I (mod n), where Q is the Fibonacci matrix {{1,1},{1,0}} and I is the identity matrix. The identity is also true for the primes congruent to 1 or 4 (mod 5), which is sequence A045468. The period of Q^k (mod n) is the same as the period of the Fibonacci numbers F(k) (mod n), A001175. Hence the terms in this sequence are the composite n such that A001175(n) divides n-1. [T. D. Noe, Jan 09 2009]
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..1000 (first 200 terms from T. D. Noe)
Eric Weisstein, MathWorld: Fibonacci Q-Matrix.
MATHEMATICA
Select[Range[2, 50000], ! PrimeQ[ # ] && Mod[Fibonacci[ # - 1], # ] == 0 && Mod[Lucas[ # ] - 1, # ] == 0 &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric Rowland, May 01 2004
EXTENSIONS
More terms from Ryan Propper, Sep 24 2005
STATUS
approved