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A047930 Smallest positive Fibonacci number divisible by n. 6
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 (list; graph; refs; listen; history; text; internal format)
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

T. D. Noe and 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 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 * A073875 A220395 A160099

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

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Last modified September 25 12:56 EDT 2017. Contains 292469 sequences.