A082117 Fibonacci sequence (mod 6).

0, 1, 1, 2, 3, 5, 2, 1, 3, 4, 1, 5, 0, 5, 5, 4, 3, 1, 4, 5, 3, 2, 5, 1, 0, 1, 1, 2, 3, 5, 2, 1, 3, 4, 1, 5, 0, 5, 5, 4, 3, 1, 4, 5, 3, 2, 5, 1, 0, 1, 1, 2, 3, 5, 2, 1, 3, 4, 1, 5, 0, 5, 5, 4, 3, 1, 4, 5, 3, 2, 5, 1, 0, 1, 1, 2, 3, 5, 2, 1, 3, 4, 1, 5, 0, 5, 5, 4, 3, 1, 4, 5, 3, 2, 5, 1, 0, 1, 1, 2, 3, 5, 2

Offset

0,4

Links

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

Glen Joyce C. Dulatre, Jamilah V. Alarcon, Vhenedict M. Florida, Daisy Ann A. Disu, On Fractal Sequences, DMMMSU-CAS Science Monitor (2016-2017) Vol. 15 No. 2, 109-113.

Syamsudhuha Muslim, Sri Gemawati, The Identity of Fibonacci Numbers Z6, International Mathematical Forum, Vol. 13, 2018, no. 5, 225-231.

Eric Weisstein's World of Mathematics, Fibonacci Number

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

Formula

Sequence is periodic with Pisano period 24 = A001175(6).

G.f.: -x*(x^22 + 5*x^21 + 2*x^20 + 3*x^19 + 5*x^18 + 4*x^17 + x^16 + 3*x^15 + 4*x^14 + 5*x^13 + 5*x^12 + 5*x^10 + x^9 + 4*x^8 + 3*x^7 + x^6 + 2*x^5 + 5*x^4 + 3*x^3 + 2*x^2 + x + 1)/((x - 1)*(x + 1)*(x^2 - x + 1)*(x^2 + 1)*(x^2 + x + 1)*(x^4 - x^2 + 1)*(x^4 + 1)*(x^8 - x^4 + 1)). - Colin Barker, Aug 15 2012

Mathematica

Table[Mod[Fibonacci[n], 6], {n, 0, 100}] (* Alonso del Arte, Jul 29 2013 *)

Prog

(Magma) [Fibonacci(n) mod 6: n in [0..100]]; // Vincenzo Librandi, Feb 04 2014
(PARI) a(n)=fibonacci(n)%6 \\ Charles R Greathouse IV, Oct 07 2016

Crossrefs

Cf. A011655, A082115, A079343, A082116, A082117, A079344.

Sequence in context: A280185 A369060 A369686 * A269701 A011157 A205387

Adjacent sequences: A082114 A082115 A082116 * A082118 A082119 A082120

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 03 2003

Extensions

Added a(0)=0 from Vincenzo Librandi, Feb 04 2014

Status

approved