This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A069705 #82 Sep 29 2024 09:20:40
%S A069705 1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,
%T A069705 2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,
%U A069705 4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4
%N A069705 a(n) = 2^n mod 7.
%C A069705 Periodic sequence with period [1,2,4]. - _Philippe Deléham_, Sep 25 2006
%C A069705 From _Klaus Brockhaus_, May 23 2010: (Start)
%C A069705 Continued fraction expansion of (11 + sqrt(229))/18.
%C A069705 Decimal expansion of 124/999. (End)
%H A069705 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F A069705 n=0 mod 3 -> a(n)=1 n=1 mod 3 -> a(n)=2 n=2 mod 3 -> a(n)=4.
%F A069705 a(n) = 2^(n mod 3). - _Paul Barry_, Oct 06 2003
%F A069705 a(n) = cubefree part of 2^n = A000079(A050985(n)). - _Artur Jasinski_, Oct 15 2008
%F A069705 From _R. J. Mathar_, Apr 13 2010: (Start)
%F A069705 a(n) = a(n-3).
%F A069705 G.f.: (1+2*x+4*x^2)/((1-x) * (1+x+x^2)). (End)
%F A069705 a(n) = (7+5*cos(2*(n+1)*Pi/3)-sqrt(3)*sin(2*(n+1)*Pi/3))/3. - _Wesley Ivan Hurt_, Oct 01 2017
%F A069705 From _Nicolas Bělohoubek_, Nov 11 2021: (Start)
%F A069705 a(n) = 8/(a(n-2)*a(n-1)).
%F A069705 a(n) = 7 - a(n-2) - a(n-1). See also A052901 or A144437. (End)
%F A069705 a(n) = n + 1 + floor((n+1)/3) - 4*floor(n/3). - _Ridouane Oudra_, Sep 25 2024
%F A069705 E.g.f.: (7*exp(x) - 2*exp(-x/2)*(2*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2)))/3. - _Stefano Spezia_, Sep 27 2024
%e A069705 a(4)=16 mod 7=2, a(5)=32 mod 7=4, a(6)=64 mod 7=1.
%p A069705 A069705 := proc(n) op((n mod 3)+1,[1,2,4]) ; end proc: # _R. J. Mathar_, Feb 05 2011
%t A069705 PowerMod[2,Range[0,110],7] (* or *) PadRight[{},110,{1,2,4}] (* _Harvey P. Dale_, Mar 28 2015 *)
%o A069705 (Sage) [power_mod(2,n,7) for n in range(0, 105)] # _Zerinvary Lajos_, Jun 07 2009
%o A069705 (PARI) a(n)=2^(n%3)%7 \\ _Charles R Greathouse IV_, Jun 11 2015
%o A069705 (PARI) a(n) = lift(Mod(2, 7)^n); \\ _Altug Alkan_, Mar 25 2016
%o A069705 (Magma) [Modexp(2, n, 7): n in [0..100]]; // _Vincenzo Librandi_, Mar 25 2016
%o A069705 (GAP) List([0..83],n->PowerMod(2,n,7)); # _Muniru A Asiru_, Jan 31 2019
%Y A069705 Cf. A000079, A050985.
%Y A069705 Cf. A178233 (decimal expansion of (11+sqrt(229))/18).
%Y A069705 Cf. A052901, A144437.
%K A069705 nonn,easy
%O A069705 0,2
%A A069705 _Jon Perry_, Jan 14 2003