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 A079344 #49 Feb 16 2025 08:32:48
%S A079344 0,1,1,2,3,5,0,5,5,2,7,1,0,1,1,2,3,5,0,5,5,2,7,1,0,1,1,2,3,5,0,5,5,2,
%T A079344 7,1,0,1,1,2,3,5,0,5,5,2,7,1,0,1,1,2,3,5,0,5,5,2,7,1,0,1,1,2,3,5,0,5,
%U A079344 5,2,7,1,0,1,1,2,3,5,0,5,5,2,7,1,0,1,1,2,3,5,0,5,5,2,7,1,0,1,1,2,3,5,0,5,5
%N A079344 F(n) mod 8, where F(n) = A000045(n) is the n-th Fibonacci number.
%C A079344 This sequence does not contain the complete set of residues modulo 8. See A079002. - _Michel Marcus_, Jan 31 2020
%H A079344 Vincenzo Librandi, <a href="/A079344/b079344.txt">Table of n, a(n) for n = 0..1000</a>
%H A079344 Brandon Avila and Yongyi Chen, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/51-2/AvilaChen.pdf">On Moduli For Which the Lucas Numbers Contain a Complete Residue System</a>, Fibonacci Quart. 51 (2013), no. 2, 151-152. See p. 151.
%H A079344 S. A. Burr, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/9-5/burr.pdf">On moduli for which the Fibonacci sequence contains a complete system of residues</a>, The Fibonacci Quarterly, 9.5 (1971), 497-504.
%H A079344 P. Ribenboim, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/43-1/paper43-1-1.pdf">FFF (Favorite Fibonacci Flowers)</a>, Fib. Q. 43 (No. 1, 2005), 3-14.
%H A079344 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci Number</a>
%H A079344 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,-1,1,0,0,-1,1).
%F A079344 Sequence is periodic with Pisano period 12 = A001175(8).
%F A079344 G.f.: -x*(1+x^2+x^3+3*x^4+6*x^6-5*x^5+x^7) / ( (x-1)*(x^2-x+1)*(1+x+x^2)*(x^4-x^2+1) ). - _R. J. Mathar_, Aug 08 2012
%e A079344 a(8) = F(8) mod 8 = 21 mod 8 = 5.
%t A079344 Mod[Fibonacci[Range[0,110]],8] (* or *) LinearRecurrence[ {1,0,0,-1,1,0,0,-1,1},{0,1,1,2,3,5,0,5,5},110] (* _Harvey P. Dale_, Jan 16 2014 *)
%o A079344 (PARI) for (n=0,100,print1(fibonacci(n)%8","))
%o A079344 (Magma) [Fibonacci(n) mod 8: n in [0..100]]; // _Vincenzo Librandi_, Feb 04 2014
%Y A079344 Cf. A000045, A011655, A082115, A079343, A082116, A082117, A079344, A079345, A111958, A079002.
%K A079344 nonn,easy
%O A079344 0,4
%A A079344 _Jon Perry_, Jan 04 2003
%E A079344 Edited by _N. J. A. Sloane_, Dec 06 2008 at the suggestion of _R. J. Mathar_