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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A082115 Fibonacci sequence (mod 3). 12
0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Fibonacci Number

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 1).

FORMULA

Sequence is periodic with Pisano period 8.

a(n) = (1/224)*{-19*(n mod 8)+37*[(n+1) mod 8]+37*[(n+2) mod 8]+9*[(n+3) mod 8]-47*[(n+4) mod 8]+65*[(n+5) mod 8]-19*[(n+6) mod 8]+9*[(n+7) mod 8]}. - Paolo P. Lava, Nov 21 2006

a(n) = 1-floor(n/8)+floor((n-1)/8)+floor((n-3)/8)-2*floor((n-4)/8) +2*floor((n-5)/8)-floor((n-7)/8). - Hieronymus Fischer, Jul 01 2007

a(n) = 1+((n mod 8)+((n+1)mod 8)-2*((n+3)mod 8)+2*((n+4)mod 8) -((n+5)mod 8) -((n+7)mod 8))/8. - Hieronymus Fischer, Jul 01 2007

G.f.: (x+x^2+2x^3+2x^5+2x^6+x^7)/(1-x^8). - Hieronymus Fischer, Jul 01 2007

a(n) = A131295(n) mod 3 (for n>0). - Hieronymus Fischer, Jul 01 2007

MATHEMATICA

f[n_]:=Mod[Fibonacci[n], 3]; lst={}; Do[AppendTo[lst, f[n]], {n, 6!}]; lst - Vladimir Joseph Stephan Orlovsky, Feb 18 2010

Table[Mod[Fibonacci[n], 3], {n, 0, 100}](* Vincenzo Librandi, Feb 04 2014 *)

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 1, 2, 0, 2, 2, 1}, 103] (* Ray Chandler, Aug 27 2015 *)

PROG

(MAGMA) [Fibonacci(n) mod 3: n in [0..100]]; // Vincenzo Librandi, Feb 04 2014

(PARI) a(n)=fibonacci(n%8)%3 \\ Charles R Greathouse IV, Sep 28 2015

CROSSREFS

Cf. A011655, A079343, A082116, A082117, A105870, A079344.

Sequence in context: A138231 A155100 A076880 * A161553 A256232 A099751

Adjacent sequences:  A082112 A082113 A082114 * A082116 A082117 A082118

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Apr 03 2003

EXTENSIONS

Added a(0)=0. - Jon Perry, Sep 15 2013

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 22:37 EST 2019. Contains 329782 sequences. (Running on oeis4.)