A069107 Composite numbers k that divide Fibonacci(k+1).

323, 377, 2834, 3827, 5777, 6479, 10877, 11663, 18407, 19043, 20999, 23407, 25877, 27323, 34943, 35207, 39203, 44099, 47519, 50183, 51983, 53663, 60377, 65471, 75077, 78089, 79547, 80189, 81719, 82983, 84279, 84419, 86063, 90287, 94667

Offset

1,1

Comments

Primes p congruent to +2 or -2 (mod 5) divide Fibonacci(p+1) (cf. A003631 and [Hardy and Wright]).

References

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.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..2000 (n = 1..250 from Reinhard Zumkeller, n = 251..1000 from Giovanni Resta)

Formula

Fibonacci(2*a(n)) mod a(n) = a(n) - 1. - Gary Detlefs, May 26 2014

Mathematica

Select[Range[2, 100000], !PrimeQ[#]&&Divisible[Fibonacci[#+1], #]&] (* Harvey P. Dale, Sep 18 2011 *)

Prog

(Haskell)
a069107 n = a069107_list !! (n-1)
a069107_list = h 2 $ drop 3 a000045_list where
   h n (fib:fibs) = if fib `mod` n > 0 || a010051 n == 1
       then h (n+1) fibs else n : h (n+1) fibs
-- Reinhard Zumkeller, Oct 13 2011
(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

Crossrefs

Cf. A045468, A003631, A064739, A081264 (Fibonacci pseudoprimes).

Cf. A000045, A010051, A023172, A069104.

Sequence in context: A339517 A217120 A081264 * A094412 A182504 A177745

Adjacent sequences: A069104 A069105 A069106 * A069108 A069109 A069110

Keyword

nice,nonn

Author

Benoit Cloitre, Apr 06 2002

Extensions

Corrected by Ralf Stephan, Oct 17 2002

Status

approved