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 A069705 a(n) = 2^n mod 7. 16
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Periodic sequence with period [1,2,4]. - Philippe Deléham, Sep 25 2006 a(n) = cubefree part of 2^n. - Artur Jasinski, Oct 15 2008 From Klaus Brockhaus, May 23 2010: (Start) Continued fraction expansion of (11 + sqrt(229))/18. Decimal expansion of 124/999. (End) LINKS Table of n, a(n) for n=0..104. Index entries for linear recurrences with constant coefficients, signature (0,0,1). FORMULA n=0 mod 3 -> a(n)=1 n=1 mod 3 -> a(n)=2 n=2 mod 3 -> a(n)=4. a(n) = 2^(n mod 3). - Paul Barry, Oct 06 2003 From R. J. Mathar, Apr 13 2010: (Start) a(n) = a(n-3). G.f.: (1+2*x+4*x^2)/((1-x) * (1+x+x^2)). (End) 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 From Nicolas Bělohoubek, Nov 11 2021: (Start) a(n) = 8/(a(n-2)*a(n-1)). a(n) = 7 - a(n-2) - a(n-1). See also A052901 or A144437. (End) EXAMPLE a(4)=16 mod 7=2, a(5)=32 mod 7=4, a(6)=64 mod 7=1. MAPLE A069705 := proc(n) op((n mod 3)+1, [1, 2, 4]) ; end proc: # R. J. Mathar, Feb 05 2011 MATHEMATICA PowerMod[2, Range[0, 110], 7] (* or *) PadRight[{}, 110, {1, 2, 4}] (* Harvey P. Dale, Mar 28 2015 *) PROG (Sage) [power_mod(2, n, 7) for n in range(0, 105)] # Zerinvary Lajos, Jun 07 2009 (PARI) a(n)=2^(n%3)%7 \\ Charles R Greathouse IV, Jun 11 2015 (PARI) a(n) = lift(Mod(2, 7)^n); \\ Altug Alkan, Mar 25 2016 (Magma) [Modexp(2, n, 7): n in [0..100]]; // Vincenzo Librandi, Mar 25 2016 (GAP) List([0..83], n->PowerMod(2, n, 7)); # Muniru A Asiru, Jan 31 2019 CROSSREFS Cf. A145642. - Artur Jasinski, Oct 15 2008 Cf. A178233 (decimal expansion of (11+sqrt(229))/18). - Klaus Brockhaus, May 23 2010 Appears in A179132. - Johannes W. Meijer, Jul 01 2010 Sequence in context: A227184 A124911 A132954 * A375030 A106645 A115314 Adjacent sequences: A069702 A069703 A069704 * A069706 A069707 A069708 KEYWORD nonn,easy AUTHOR Jon Perry, Jan 14 2003 STATUS approved

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Last modified August 11 23:45 EDT 2024. Contains 375082 sequences. (Running on oeis4.)