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 A082117 Fibonacci sequence (mod 6). 10

%I

%S 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,

%T 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,

%U 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

%N Fibonacci sequence (mod 6).

%H Vincenzo Librandi, <a href="/A082117/b082117.txt">Table of n, a(n) for n = 0..1000</a>

%H Glen Joyce C. Dulatre, Jamilah V. Alarcon, Vhenedict M. Florida, Daisy Ann A. Disu, <a href="http://www.dmmmsu-sluc.com/wp-content/uploads/2018/03/CAS-Monitor-2016-2017-1.pdf">On Fractal Sequences</a>, DMMMSU-CAS Science Monitor (2016-2017) Vol. 15 No. 2, 109-113.

%H Syamsudhuha Muslim, Sri Gemawati, <a href="https://doi.org/10.12988/imf.2018.827">The Identity of Fibonacci Numbers Z6</a>, International Mathematical Forum, Vol. 13, 2018, no. 5, 225-231.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci Number</a>

%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, 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).

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

%F 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

%t Table[Mod[Fibonacci[n], 6], {n, 0, 100}] (* _Alonso del Arte_, Jul 29 2013 *)

%o (MAGMA) [Fibonacci(n) mod 6: n in [0..100]]; // _Vincenzo Librandi_, Feb 04 2014

%o (PARI) a(n)=fibonacci(n)%6 \\ _Charles R Greathouse IV_, Oct 07 2016

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

%K nonn,easy

%O 0,4

%A _Eric W. Weisstein_, Apr 03 2003

%E Added a(0)=0 from _Vincenzo Librandi_, Feb 04 2014

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)