A204689 a(n) = n^n (mod 4).

1, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0

Offset

0,4

Comments

Apart from a(0), the same as A109718. [Joerg Arndt, Sep 17 2013]

Periodic for n>0 with period 4 = A174824(4): repeat [1, 0, 3, 0].

Links

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

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

Formula

From Bruno Berselli, Jan 18 2012: (Start)

G.f.: (1+x+3x^3-x^4)/(1-x^4).

a(n) = (1-(-1)^n)*(2+i^(n+1))/2 with i=sqrt(-1), a(0)=1.

a(n) = A109718(n) for n>0. (End)

a(2k) = A000007(k), a(2k+1) = A010684(k). - Wesley Ivan Hurt, Jun 15 2016

Maple

A204689:=n->n^n mod 4: seq(A204689(n), n=0..150); # Wesley Ivan Hurt, Jun 15 2016

Mathematica

Table[PowerMod[n, n, 4], {n, 0, 140}]

Prog

(Magma) [1] cat &cat [[1, 0, 3, 0]^^30]; // Wesley Ivan Hurt, Jun 15 2016

Crossrefs

Cf. A000007, A010684, A109718, A174824.

Sequence in context: A007524 A357868 A357881 * A109718 A053385 A213543

Adjacent sequences: A204686 A204687 A204688 * A204690 A204691 A204692

Keyword

nonn,easy

Author

José María Grau Ribas, Jan 18 2012

Status

approved