A082115 Fibonacci sequence (mod 3).

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

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-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

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 A366444 A256232

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