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!)
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

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