A204688 a(n) = n^n (mod 3).

1, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1

Offset

0,6

Comments

For n>0, a(n) is periodic with period 6: repeat [1, 1, 0, 1, 2, 0].

Decimal expansion of 1110119/9999990. - David A. Corneth, Jun 28 2016

Links

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

José María Grau and Antonio M. Oller-Marcén, On the last digit and the last non-zero digit of n^n in base b, arXiv preprint arXiv:1203.4066 [math.NT], 2012.

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

Formula

G.f.: (1+x+x^2+x^4+2*x^5-x^6) / (1-x^6). - Bruno Berselli, Jan 18 2012

From Wesley Ivan Hurt, Jun 28 2016: (Start)

a(n) = a(n-6) for n>6.

a(n) = sin(n*Pi/3) * (10*sin(n*Pi/3) + 2*sin(2*n*Pi/3) - sqrt(3) - 2*sqrt(3)*cos(n*Pi/3))/6 for n>0. (End)

a(n) = A010872(A000312(n)). - Michel Marcus, Jun 28 2016

Maple

A204688:=n->power(n, n) mod 3: 1, seq(A204688(n), n=1..100); # Wesley Ivan Hurt, Jun 28 2016

Mathematica

Table[PowerMod[n, n, 3], {n, 0, 140}]

Prog

(Magma) [1] cat [Modexp(n, n, 3): n in [1..100]]; // Wesley Ivan Hurt, Jun 28 2016

Crossrefs

Cf. A000312, A010872, A174824.

Sequence in context: A060277 A333330 A290825 * A332038 A101672 A083731

Adjacent sequences: A204685 A204686 A204687 * A204689 A204690 A204691

Keyword

nonn,easy

Author

José María Grau Ribas, Jan 18 2012

Status

approved