A185057 a(n) = n^n! (mod 5).

0, 1, 4, 4, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1

Offset

0,3

Comments

For n > 3, periodic with period 5: repeat [1, 0, 1, 1, 1].

Links

Table of n, a(n) for n=0..84.

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

Formula

a(n) = (2/5)*(2 - cos(2*n*Pi/5) - cos(4*n*Pi/5)) for n > 3. - Wesley Ivan Hurt, Sep 27 2018

Mathematica

Table[PowerMod[n, n!, 5], {n, 0, 84}]
Join[{0, 1, 4, 4}, LinearRecurrence[{0, 0, 0, 0, 1}, {1, 0, 1, 1, 1}, 81]] (* Ray Chandler, Aug 25 2015 *)
PadRight[{0, 1, 4, 4}, 120, {0, 1, 1, 1, 1}] (* Harvey P. Dale, Dec 22 2022 *)

Crossrefs

Sequence in context: A366467 A366464 A373749 * A343720 A048152 A350037

Adjacent sequences: A185054 A185055 A185056 * A185058 A185059 A185060

Keyword

nonn,easy

Author

José María Grau Ribas, Jan 21 2012

Status

approved