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%I #16 Oct 30 2023 07:47:16
%S 2737,4181,6721,13201,15251,34561,51841,64079,64681,67861,68251,90061,
%T 96049,97921,118441,146611,163081,179697,186961,194833,197209,219781,
%U 252601,254321,257761,268801,272611,283361,302101,303101,327313,330929
%N Composite n such that n divides both Fibonacci(n-1) and Fibonacci(n) - 1.
%C 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]
%H Giovanni Resta, <a href="/A094401/b094401.txt">Table of n, a(n) for n = 1..1000</a> (first 200 terms from T. D. Noe)
%H Eric Weisstein, <a href="http://mathworld.wolfram.com/FibonacciQ-Matrix.html">MathWorld: Fibonacci Q-Matrix</a>.
%t Select[Range[2, 50000], ! PrimeQ[ # ] && Mod[Fibonacci[ # - 1], # ] == 0 && Mod[Lucas[ # ] - 1, # ] == 0 &]
%Y Cf. A005845, A069106, A094394, A094400.
%K nonn
%O 1,1
%A _Eric Rowland_, May 01 2004
%E More terms from _Ryan Propper_, Sep 24 2005