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

1,2

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

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.

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000045, A001177, A037943.

Sequence in context: A051696 A066570 A073656 * A349100 A073875 A356883

Adjacent sequences: A047927 A047928 A047929 * A047931 A047932 A047933

Keyword

easy,nice,nonn

Author

J. Lowell

Extensions

More terms from Patrick De Geest, Jun 15 1999

Status

approved