A204695 a(n) = n^n (mod 9).

1, 1, 4, 0, 4, 2, 0, 7, 1, 0, 1, 5, 0, 4, 7, 0, 7, 8, 0, 1, 4, 0, 4, 2, 0, 7, 1, 0, 1, 5, 0, 4, 7, 0, 7, 8, 0, 1, 4, 0, 4, 2, 0, 7, 1, 0, 1, 5, 0, 4, 7, 0, 7, 8, 0, 1, 4, 0, 4, 2, 0, 7, 1, 0, 1, 5, 0, 4, 7, 0, 7, 8, 0, 1, 4, 0, 4, 2, 0, 7, 1, 0, 1, 5, 0, 4, 7

Offset

0,3

Comments

For n>0, periodic with period 18 = A174824(9): repeat [1, 4, 0, 4, 2, 0, 7, 1, 0, 1, 5, 0, 4, 7, 0, 7, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Formula

G.f.: (x^18 - 8*x^17 - 7*x^16 - 7*x^14 - 4*x^13 - 5*x^11 - x^10 - x^8 - 7*x^7 - 2*x^5 - 4*x^4 - 4*x^2 - x - 1)/(x^18 - 1). - Chai Wah Wu, Jun 04 2016

a(n) = A000312(n) mod 9. - Michel Marcus, Jun 04 2016

Mathematica

Table[PowerMod[n, n, 9], {n, 0, 100}]
Join[{1}, LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 4, 0, 4, 2, 0, 7, 1, 0, 1, 5, 0, 4, 7, 0, 7, 8, 0}, 86]] (* Ray Chandler, Aug 27 2015 *)

Prog

(PARI) a(n)=lift(Mod(n, 9)^n) \\ Charles R Greathouse IV, Jan 23 2012

Crossrefs

Cf. A000312, A174824.

Sequence in context: A010636 A222302 A222617 * A175435 A160214 A081087

Adjacent sequences: A204692 A204693 A204694 * A204696 A204697 A204698

Keyword

nonn,easy

Author

José María Grau Ribas, Jan 18 2012

Status

approved