A204694 a(n) = n^n (mod 8).

1, 1, 4, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0

Offset

0,3

Comments

Eventually periodic with period 8 = A174824(8): a(1)=1, a(2)=4 and repeat [3, 0, 5, 0, 7, 0, 1, 0].

Links

Table of n, a(n) for n=0..86.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 1).

Formula

G.f.: (4*x^10 + x^8 - 7*x^7 - 5*x^5 - 3*x^3 - 4*x^2 - x - 1)/(x^8 - 1). - Chai Wah Wu, Jun 04 2016

a(n) = A000312(n) mod 8. - Michel Marcus, Jun 04 2016

Mathematica

Table[PowerMod[n, n, 8], {n, 0, 100}]
Join[{1, 1, 4}, LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1}, {3, 0, 5, 0, 7, 0, 1, 0}, 84]] (* Ray Chandler, Aug 25 2015 *)
PadRight[{1, 1, 4}, 120, {0, 1, 0, 3, 0, 5, 0, 7}] (* Harvey P. Dale, Aug 06 2018 *)

Prog

(PARI) a(n)=lift(Mod(n, 8)^n) \\ Charles R Greathouse IV, Jan 23 2012

Crossrefs

Cf. A000312, A174824.

Sequence in context: A016697 A086466 A330392 * A304030 A338802 A242721

Adjacent sequences: A204691 A204692 A204693 * A204695 A204696 A204697

Keyword

nonn,easy

Author

José María Grau Ribas, Jan 18 2012

Status

approved