login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A066853 Number of different remainders (or residues) for the Fibonacci numbers (A000045) when divided by n (i.e., the size of the set of F(i) mod n over all i). 12
1, 2, 3, 4, 5, 6, 7, 6, 9, 10, 7, 11, 9, 14, 15, 11, 13, 11, 12, 20, 9, 14, 19, 13, 25, 18, 27, 21, 10, 30, 19, 21, 19, 13, 35, 15, 29, 13, 25, 30, 19, 18, 33, 20, 45, 21, 15, 15, 37, 50, 35, 30, 37, 29, 12, 25, 33, 20, 37, 55, 25, 21, 23, 42, 45, 38, 51, 20, 29, 70, 44, 15, 57 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The Fibonacci numbers mod n for any n are periodic - see A001175 for period lengths. - Ron Knott, Jan 05 2005

a(n) = number of nonzeros in n-th row of triangle A128924. - Reinhard Zumkeller, Jan 16 2014

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

Casey Mongoven, Sonification of multiple Fibonacci-related sequences, Annales Mathematicae et Informaticae, 41 (2013) pp. 175-192.

EXAMPLE

a(8)=6 since the Fibonacci numbers, 0,1,1,2,3,5,8,13,21,34,55,89,144,... when divided by 8 have remainders 0,1,1,2,3,5,0,5,5,2,7,1 (repeatedly) which only contains the remainders 0,1,2,3,5 and 7, i.e., 6 remainders, so a(8)=6.

a(11)=7 since Fibonacci numbers reduced modulo 11 are {0, 1, 2, 3, 5, 8, 10}.

PROG

(Haskell)

a066853 1 = 1

a066853 n = f 1 ps [] where

   f 0 (1 : xs) ys = length ys

   f _ (x : xs) ys = if x `elem` ys then f x xs ys else f x xs (x:ys)

   ps = 1 : 1 : zipWith (\u v -> (u + v) `mod` n) (tail ps) ps

-- Reinhard Zumkeller, Jan 16 2014

(PARI) a(n)=if(n<8, return(n)); my(v=List([1, 2])); while(v[#v]!=1 || v[#v-1]!=0, listput(v, (v[#v]+v[#v-1])%n)); #Set(v) \\ Charles R Greathouse IV, Jun 19 2017

CROSSREFS

Cf. A001175, A079002.

Sequence in context: A005599 A071934 A161658 * A264856 A141258 A117656

Adjacent sequences:  A066850 A066851 A066852 * A066854 A066855 A066856

KEYWORD

nonn

AUTHOR

Reiner Martin (reinermartin(AT)hotmail.com), Jan 21 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified September 26 10:46 EDT 2017. Contains 292518 sequences.