A047930 Smallest positive Fibonacci number divisible by n.

1, 2, 3, 8, 5, 144, 21, 8, 144, 610, 55, 144, 13, 46368, 6765, 144, 34, 144, 2584, 832040, 21, 832040, 46368, 144, 75025, 10946, 14930352, 46368, 377, 1548008755920, 832040, 46368, 6765, 34, 102334155, 144, 4181, 2584, 317811, 832040, 6765, 46368, 701408733

Offset: 1

Author

J. Lowell

Keywords

• easy
• nice
• nonn

Comments

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

Note that F(0)=0 is divisible by any n > 0, hence "positive" is added in NAME. - Zak Seidov, Jan 07 2016

Examples

			Fibonacci(12) = 144 is the first Fibonacci number that is divisible by 6, so a(6) = 144.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 500 terms from T. D. Noe)
• Samin Riasat, Z[phi] and the Fibonacci Sequence Modulo n, Mathematical Reflections 1 (2011) pp. 1-7.

Crossrefs

Cf. A000045, A001177, A037943.

Programs

Mathematica

With[{fibs = Fibonacci[Range[150]]}, Flatten[Table[Select[fibs, Divisible[#, n] &, 1], {n, 60}]]] (* Harvey P. Dale, Oct 20 2011 *)

PARI

a(n)=my(k); while(fibonacci(k++)%n,); fibonacci(k) \\ Charles R Greathouse IV, Feb 04 2014

Formula

a(A000045(k)) = A000045(k), for k > 0. - Altug Alkan, Jan 07 2016

a(n) = n * A037943(n). - Alois P. Heinz, Jan 08 2017

Extensions

More terms from Patrick De Geest, Jun 15 1999