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

Author

José María Grau Ribas, Jan 18 2012

Keywords

• nonn
• easy

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

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

Crossrefs

Cf. A000312, A174824.

Programs

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 *)

PARI

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

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