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A204671 a(n) = n^n (mod 6). 3
1, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
For n>0, periodic with period 6 = A174824: repeat [1, 4, 3, 4, 5, 0].
LINKS
FORMULA
G.f.: (x^6-5*x^5-4*x^4-3*x^3-4*x^2-x-1)/((x-1)*(x+1)*(x^2-x+1)*(x^2+x+1)). [Colin Barker, Jul 20 2012]
From Wesley Ivan Hurt, Jun 23 2016: (Start)
a(n) = a(n-6) for n>5.
a(0) = 1, a(n) = (17 - cos(n*Pi) - 8*cos(n*Pi/3) - 8*cos(2*n*Pi/3) - 4*sqrt(3)*sin(n*Pi/3) - 4*sqrt(3)*sin(2*n*Pi/3))/6 for n>0. (End)
a(n) = A010875(A000312(n)). - Michel Marcus, Jun 27 2016
MAPLE
A204671:=n->[1, 4, 3, 4, 5, 0][(n mod 6)+1]: 1, seq(A204671(n), n=0..100); # Wesley Ivan Hurt, Jun 23 2016
MATHEMATICA
Table[PowerMod[n, n, 6], {n, 0, 140}]
Join[{1}, LinearRecurrence[{0, 0, 0, 0, 0, 1}, {1, 4, 3, 4, 5, 0}, 86]] (* Ray Chandler, Aug 26 2015 *)
PROG
(Magma) [1] cat &cat [[1, 4, 3, 4, 5, 0]^^20]; // Wesley Ivan Hurt, Jun 23 2016
(PARI) a(n)=lift(Mod(n, 6)^n) \\ Andrew Howroyd, Feb 25 2018
CROSSREFS
Sequence in context: A332472 A049788 A002558 * A204816 A204818 A099634
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified May 28 01:34 EDT 2024. Contains 372900 sequences. (Running on oeis4.)