login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A079344 F(n) mod 8, where F(n) = A000045(n) is the n-th Fibonacci number. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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).

a(n) = (1/396)*{-17*(n mod 12)+49*[(n+1) mod 12]+214*[(n+2) mod 12]-149*[(n+3) mod 12]+115*[(n+4) mod 12]+16*[(n+5) mod 12]-149*[(n+6) mod 12]+181*[(n+7) mod 12]-50*[(n+8) mod 12]-17*[(n+9) mod 12]-17*[(n+10) mod 12]+16*[(n+11) mod 12]} with n>=0. - Paolo P. Lava, Nov 24 2006

a(n) = (1/396)*{49*[n mod 12] + 214*[(n + 1) mod 12] - 149*[(n + 2) mod 12] + 115*[(n + 3) mod 12] + 16*[(n + 4) mod 12] - 149*[(n + 5) mod 12] + 181*[(n + 6) mod 12] - 50*[(n + 7) mod 12] - 17*[(n + 8) mod 12] - 17*[(n + 9) mod 12] + 16*[(n + 10) mod 12] - 17*[(n + 11) mod 12]}, with n>= 0. - Paolo P. Lava, May 30 2007

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

a={}; Do[f=Fibonacci[n]; AppendTo[a, Mod[f, 8]], {n, 1, 30}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)

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.

Sequence in context: A039705 A254271 A082118 * A096535 A126047 A023049

Adjacent sequences:  A079341 A079342 A079343 * A079345 A079346 A079347

KEYWORD

nonn,easy

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 13 03:41 EST 2019. Contains 329968 sequences. (Running on oeis4.)