A070341 a(n) = 3^n mod 11: Repeat (1, 3, 9, 5, 4), period 5.

1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9, 5, 4, 1, 3, 9

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Comments

Simple continued fraction expansion of 13/24 + sqrt(8761)/120 = 1.3216684472... - R. J. Mathar, Mar 08 2012

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 1).

Programs

Mathematica

PowerMod[3,Range[0,100],11] (* or *) PadRight[{},100,{1,3,9,5,4}] (* Harvey P. Dale, Feb 05 2012 *)

PARI

a(n)=lift(Mod(3,11)^n)

PARI

a(n)=[1, 3, 9, 5, 4][n%5+1]  \\ M. F. Hasler, Mar 04 2011

Sage

[power_mod(3, n, 11)for n in range(0, 93)] # Zerinvary Lajos, Nov 24 2009

Formula

From R. J. Mathar, Apr 13 2010: (Start)

a(n) = a(n-5).

G.f.: (1+3*x+9*x^2+5*x^3+4*x^4)/ ((1-x) * (1+x+x^2+x^3+x^4)). (End)