A070347 a(n) = 2^n mod 21.

1, 2, 4, 8, 16, 11, 1, 2, 4, 8, 16, 11, 1, 2, 4, 8, 16, 11, 1, 2, 4, 8, 16, 11, 1, 2, 4, 8, 16, 11, 1, 2, 4, 8, 16, 11, 1, 2, 4, 8, 16, 11, 1, 2, 4, 8, 16, 11, 1, 2, 4, 8, 16, 11, 1, 2, 4, 8, 16, 11, 1, 2, 4, 8, 16, 11, 1, 2, 4, 8, 16, 11, 1, 2, 4, 8, 16, 11, 1, 2, 4, 8, 16, 11, 1, 2, 4, 8, 16, 11

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Links

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

Programs

GAP

List([0..83],n->PowerMod(2,n,21)); # Muniru A Asiru, Jan 31 2019

Mathematica

PowerMod[2, Range[0, 50], 21] (* G. C. Greubel, Mar 11 2016 *)
LinearRecurrence[{1,-1,1,-1,1},{1,2,4,8,16},120] (* or *) PadRight[{},120,{1,2,4,8,16,11}] (* Harvey P. Dale, Mar 19 2016 *)

PARI

a(n)=lift(Mod(2,21)^n) \\ Charles R Greathouse IV, Mar 22 2016

Sage

[power_mod(2,n,21)for n in range(0,90)] # Zerinvary Lajos, Nov 03 2009

Formula

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

a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5).

G.f.: (1 + x + 3*x^2 + 5*x^3 + 11*x^4)/ ((1-x) * (1+x+x^2) * (1-x+x^2)). (End)

a(n) = a(n-6). - G. C. Greubel, Mar 11 2016