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%I #47 Dec 03 2021 00:53:52
%S 323,377,2834,3827,5777,6479,10877,11663,18407,19043,20999,23407,
%T 25877,27323,34943,35207,39203,44099,47519,50183,51983,53663,60377,
%U 65471,75077,78089,79547,80189,81719,82983,84279,84419,86063,90287,94667
%N Composite numbers k that divide Fibonacci(k+1).
%C Primes p congruent to +2 or -2 (mod 5) divide Fibonacci(p+1) (cf. A003631 and [Hardy and Wright]).
%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers (Fifth edition), Oxford Univ. Press (Clarendon), 1979, Chap. X, p. 150.
%H Chai Wah Wu, <a href="/A069107/b069107.txt">Table of n, a(n) for n = 1..2000</a> (n = 1..250 from Reinhard Zumkeller, n = 251..1000 from Giovanni Resta)
%F Fibonacci(2*a(n)) mod a(n) = a(n) - 1. - _Gary Detlefs_, May 26 2014
%t Select[Range[2,100000],!PrimeQ[#]&&Divisible[Fibonacci[#+1],#]&] (* _Harvey P. Dale_, Sep 18 2011 *)
%o (Haskell)
%o a069107 n = a069107_list !! (n-1)
%o a069107_list = h 2 $ drop 3 a000045_list where
%o h n (fib:fibs) = if fib `mod` n > 0 || a010051 n == 1
%o then h (n+1) fibs else n : h (n+1) fibs
%o -- _Reinhard Zumkeller_, Oct 13 2011
%o (PARI) is(n)=((Mod([1,1;1,0],n))^(n+1))[1,2]==0 && !isprime(n) && n>1 \\ _Charles R Greathouse IV_, Oct 07 2016
%Y Cf. A045468, A003631, A064739, A081264 (Fibonacci pseudoprimes).
%Y Cf. A000045, A010051, A023172, A069104.
%K nice,nonn
%O 1,1
%A _Benoit Cloitre_, Apr 06 2002
%E Corrected by _Ralf Stephan_, Oct 17 2002