A185058 a(n) = n^n! mod 7.

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

Offset

0,3

Comments

For n > 2, periodic with period 7: repeat [1, 1, 1, 1, 0, 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, 0, 0, 1).

Formula

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

a(n) = sign(n mod 7) for n > 2. - Wesley Ivan Hurt, Dec 23 2016

Maple

A185058:= n -> [0, 1, 1, 1, 1, 1, 1][(n mod 7)+1]: 0, 1, 4, seq(A185058(n), n=3..100); # Wesley Ivan Hurt, Dec 23 2016

Mathematica

Table[PowerMod[n, n!, 7], {n, 0, 84}]
Join[{0, 1, 4}, LinearRecurrence[{0, 0, 0, 0, 0, 0, 1}, {1, 1, 1, 1, 0, 1, 1}, 82]] (* Ray Chandler, Aug 26 2015 *)
PadRight[{0, 1, 4}, 120, {0, 1, 1, 1, 1, 1, 1}] (* Harvey P. Dale, May 29 2020 *)

Prog

(Magma) [0, 1, 4] cat &cat [[1, 1, 1, 1, 0, 1, 1]^^20]; // Wesley Ivan Hurt, Dec 23 2016

Crossrefs

Sequence in context: A122777 A103524 A110916 * A368474 A369935 A368169

Adjacent sequences: A185055 A185056 A185057 * A185059 A185060 A185061

Keyword

nonn,easy

Author

José María Grau Ribas, Jan 21 2012

Status

approved