A079344 F(n) mod 8, where F(n) = A000045(n) is the n-th Fibonacci number.
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, 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, 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
Offset: 0
Examples
a(8) = F(8) mod 8 = 21 mod 8 = 5.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Brandon Avila and Yongyi Chen, On Moduli For Which the Lucas Numbers Contain a Complete Residue System, Fibonacci Quart. 51 (2013), no. 2, 151-152. See p. 151.
- S. A. Burr, On moduli for which the Fibonacci sequence contains a complete system of residues, The Fibonacci Quarterly, 9.5 (1971), 497-504.
- P. Ribenboim, FFF (Favorite Fibonacci Flowers), Fib. Q. 43 (No. 1, 2005), 3-14.
- Eric Weisstein's World of Mathematics, Fibonacci Number
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,-1,1,0,0,-1,1).
Crossrefs
Programs
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Magma
[Fibonacci(n) mod 8: n in [0..100]]; // Vincenzo Librandi, Feb 04 2014
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Mathematica
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 *) -
PARI
for (n=0,100,print1(fibonacci(n)%8","))
Formula
Sequence is periodic with Pisano period 12 = A001175(8).
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
Extensions
Edited by N. J. A. Sloane, Dec 06 2008 at the suggestion of R. J. Mathar
Comments