Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #39 Nov 03 2023 00:00:43
%S 1,2,3,8,5,144,21,8,144,610,55,144,13,46368,6765,144,34,144,2584,
%T 832040,21,832040,46368,144,75025,10946,14930352,46368,377,
%U 1548008755920,832040,46368,6765,34,102334155,144,4181,2584,317811,832040,6765,46368,701408733
%N Smallest positive Fibonacci number divisible by n.
%C Corollary 1 in Riasat (2011), "every positive integer divides infinitely many Fibonacci numbers," demonstrates that this sequence is infinite. - _Alonso del Arte_, Jul 27 2013
%C Note that F(0)=0 is divisible by any n > 0, hence "positive" is added in NAME. - _Zak Seidov_, Jan 07 2016
%H Alois P. Heinz, <a href="/A047930/b047930.txt">Table of n, a(n) for n = 1..1000</a> (first 500 terms from T. D. Noe)
%H Samin Riasat, <a href="https://sriasat.files.wordpress.com/2012/12/fibonacci13.pdf">Z[phi] and the Fibonacci Sequence Modulo n</a>, Mathematical Reflections 1 (2011) pp. 1-7.
%F a(A000045(k)) = A000045(k), for k > 0. - _Altug Alkan_, Jan 07 2016
%F a(n) = n * A037943(n). - _Alois P. Heinz_, Jan 08 2017
%e Fibonacci(12) = 144 is the first Fibonacci number that is divisible by 6, so a(6) = 144.
%t With[{fibs = Fibonacci[Range[150]]}, Flatten[Table[Select[fibs, Divisible[#, n] &, 1], {n, 60}]]] (* _Harvey P. Dale_, Oct 20 2011 *)
%o (PARI) a(n)=my(k); while(fibonacci(k++)%n,); fibonacci(k) \\ _Charles R Greathouse IV_, Feb 04 2014
%Y Cf. A000045, A001177, A037943.
%K easy,nice,nonn
%O 1,2
%A _J. Lowell_
%E More terms from _Patrick De Geest_, Jun 15 1999