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

Author

José María Grau Ribas, Jan 18 2012

Keywords

• nonn
• easy

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

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

Crossrefs

Cf. A000007, A010684, A109718, A174824.

Programs

Magma

[1] cat &cat [[1, 0, 3, 0]^^30]; // 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}]

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