This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A082115 #37 Feb 16 2025 08:32:48
%S A082115 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,
%T A082115 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,
%U A082115 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
%N A082115 Fibonacci sequence (mod 3).
%H A082115 Vincenzo Librandi, <a href="/A082115/b082115.txt">Table of n, a(n) for n = 0..1000</a>
%H A082115 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci Number</a>
%H A082115 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1).
%F A082115 Sequence is periodic with Pisano period 8.
%F A082115 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
%F A082115 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
%F A082115 G.f.: (x+x^2+2x^3+2x^5+2x^6+x^7)/(1-x^8). - _Hieronymus Fischer_, Jul 01 2007
%F A082115 a(n) = A131295(n) mod 3 (for n>0). - _Hieronymus Fischer_, Jul 01 2007
%t A082115 Table[Mod[Fibonacci[n], 3], {n, 0, 100}](* _Vincenzo Librandi_, Feb 04 2014 *)
%t A082115 LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1},{0, 1, 1, 2, 0, 2, 2, 1},103] (* _Ray Chandler_, Aug 27 2015 *)
%o A082115 (Magma) [Fibonacci(n) mod 3: n in [0..100]]; // _Vincenzo Librandi_, Feb 04 2014
%o A082115 (PARI) a(n)=fibonacci(n%8)%3 \\ _Charles R Greathouse IV_, Sep 28 2015
%Y A082115 Cf. A011655, A079343, A082116, A082117, A105870, A079344.
%K A082115 nonn,easy
%O A082115 0,4
%A A082115 _Eric W. Weisstein_, Apr 03 2003
%E A082115 Added a(0)=0. - _Jon Perry_, Sep 15 2013