|
|
A082116
|
|
Fibonacci sequence (mod 5).
|
|
10
|
|
|
0, 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1, 0, 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1, 0, 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1, 0, 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1, 0, 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1, 0, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
This sequence contains the complete set of residues modulo 5. See A079002. - Michel Marcus, Jan 31 2020
|
|
REFERENCES
|
S. Vajda, Fibonacci and Lucas numbers and the Golden Section, Ellis Horwood Ltd., Chichester, 1989. See p. 88. - N. J. A. Sloane, Feb 20 2013
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (0,1,0,-1,1,1,-1,-1,1,0,-1,0,1).
|
|
FORMULA
|
Sequence is periodic with Pisano period 20.
a(n) = 2 + ((n mod 20) - ((n - 1) mod 20) - ((n - 3) mod 20) - ((n - 4) mod 20) + 3*((n - 5) mod 20) - 3*((n - 6) mod 20) + 2*((n - 8) mod 20) - 3*((n - 9) mod 20) + 4*((n - 10) mod 20) - 4*((n - 11) mod 20) + ((n - 13) mod 20) + ((n - 14) mod 20) + 2*((n - 15) mod 20) - 2*((n - 16) mod 20) - 2*((n - 18) mod 20) + 3*((n - 19) mod 20))/20. - Hieronymus Fischer, Jun 30 2007
G.f.: (x + x^2 + 2x^3 + 3x^4 + 3x^6 + 3x^7 + x^8 + 4x^9 + 4x^11 + 4x^12 + 3x^13 + 2x^14 + 2x^16 + 2x^17 + 4x^18 + x^19)/(1 - x^20), not reduced. - Hieronymus Fischer, Jun 30 2007
G.f.: -x*(1 + x + x^2 + 2*x^3 + 3*x^6 - x^7 - 2*x^8 - x^4 + x^9 + 4*x^10 + x^11) / ( (x - 1) * (x^4 + x^3 + x^2 + x + 1) * (x^8 - x^6 + x^4 - x^2 + 1) ). - R. J. Mathar, Jul 14 2012
|
|
MATHEMATICA
|
Table[Mod[Fibonacci[n], 5], {n, 0, 125}] (* Alonso del Arte, Jul 29 2013 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|