A070338 a(n) = 2^n mod 33.

1, 2, 4, 8, 16, 32, 31, 29, 25, 17, 1, 2, 4, 8, 16, 32, 31, 29, 25, 17, 1, 2, 4, 8, 16, 32, 31, 29, 25, 17, 1, 2, 4, 8, 16, 32, 31, 29, 25, 17, 1, 2, 4, 8, 16, 32, 31, 29, 25, 17, 1, 2, 4, 8, 16, 32, 31, 29, 25, 17, 1, 2, 4, 8, 16, 32, 31, 29, 25, 17, 1, 2, 4, 8

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Comments

The sequence has a cycle of length 10, which is the maximum possible length for a sequence of powers mod 33. - Alonso del Arte, Jan 12 2013

Links

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

Programs

GAP

List([0..83],n->PowerMod(2,n,33)); # Muniru A Asiru, Jan 30 2019

Mathematica

Table[Mod[2^n, 33], {n, 0, 79}] (* Alonso del Arte, Jan 12 2013 *)
PowerMod[2, Range[0, 50], 33] (* G. C. Greubel, Mar 13 2016 *)
LinearRecurrence[{1,0,0,0,-1,1},{1,2,4,8,16,32},90] (* Harvey P. Dale, Jun 26 2017 *)

PARI

a(n)=lift(Mod(2,33)^n) \\ Charles R Greathouse IV, Mar 22 2016

Sage

[power_mod(2,n,33)for n in range(0,74)] # Zerinvary Lajos, Nov 03 2009

Formula

From G. C. Greubel, Mar 13 2016: (Start)

a(n) = a(n-10).

a(n) = a(n-1) - a(n-5) + a(n-6). (End)