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

0,4

Comments

This sequence does not contain the complete set of residues modulo 8. See A079002. - Michel Marcus, Jan 31 2020

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).

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

Example

a(8) = F(8) mod 8 = 21 mod 8 = 5.

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 *)

Prog

(PARI) for (n=0, 100, print1(fibonacci(n)%8", "))
(Magma) [Fibonacci(n) mod 8: n in [0..100]]; // Vincenzo Librandi, Feb 04 2014

Crossrefs

Cf. A000045, A011655, A082115, A079343, A082116, A082117, A079344, A079345, A111958, A079002.

Sequence in context: A039705 A254271 A082118 * A096535 A126047 A023049

Adjacent sequences: A079341 A079342 A079343 * A079345 A079346 A079347

Keyword

nonn,easy,changed

Author

Jon Perry, Jan 04 2003

Extensions

Edited by N. J. A. Sloane, Dec 06 2008 at the suggestion of R. J. Mathar

Status

approved