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A070338
a(n) = 2^n mod 33.
2
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
0,2
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
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)
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 *)
PROG
(Sage) [power_mod(2, n, 33)for n in range(0, 74)] # Zerinvary Lajos, Nov 03 2009
(PARI) a(n)=lift(Mod(2, 33)^n) \\ Charles R Greathouse IV, Mar 22 2016
(GAP) List([0..83], n->PowerMod(2, n, 33)); # Muniru A Asiru, Jan 30 2019
CROSSREFS
Sequence in context: A070340 A036124 A070339 * A331380 A115423 A221467
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 12 2002
STATUS
approved