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
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).
Programs
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Magma
[Fibonacci(n) mod 6: n in [0..100]]; // Vincenzo Librandi, Feb 04 2014
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Mathematica
Table[Mod[Fibonacci[n], 6], {n, 0, 100}] (* Alonso del Arte, Jul 29 2013 *) -
PARI
a(n)=fibonacci(n)%6 \\ Charles R Greathouse IV, Oct 07 2016
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
Extensions
Added a(0)=0 from Vincenzo Librandi, Feb 04 2014