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 A153727 Period 3: repeat [1, 4, 2] ; Trajectory of 3x+1 sequence starting at 1. 12
 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS From Klaus Brockhaus, May 23 2010: (Start) Continued fraction expansion of (7+sqrt(229))/18. Decimal expansion of 142/999. (End) a(A008585(n)) = 1; a(A016777(n)) = 4; a(A016789(n)) = 2. - Reinhard Zumkeller, Oct 08 2011 REFERENCES C. A. Pickover, The Math Book, 2009; Collatz Conjecture, pp 374-375. LINKS Eric Weisstein's World of Mathematics, Collatz Problem Wikipedia, Collatz conjecture Index entries for linear recurrences with constant coefficients, signature (0, 0, 1). FORMULA a(3n)=1, a(3n+1)=4, a(3n+2)=2. G.f.: (1+4*x+2*x^2)/(1-x^3). a(n) = 4^n mod 7. - Zerinvary Lajos, Nov 25 2009 a(n) = (1/9)*{10*(n mod 3)+13*[(n+1) mod 3]-2*[(n+2) mod 3]}, with n>=0. - Paolo P. Lava, Jun 17 2009 a(n) = A130196(n) * A131534(n). - Reinhard Zumkeller, Nov 12 2009 a(n) = 2^(-n mod 3) = 2^A080425(n). - Wesley Ivan Hurt, Jun 20 2014 a(n) = sqrt(4^(5*n) mod 21). - Gary Detlefs, Jul 07 2014 From Wesley Ivan Hurt, Jun 30 2016: (Start) a(n) = a(n-3) for n>2. a(n) = (7 - 4*cos(2*n*Pi/3) + 2*sqrt(3)*sin(2*n*Pi/3))/3. (End) MAPLE A153727:=n->2^(-n mod 3); seq(A153727(n), n=0..50); # Wesley Ivan Hurt, Jun 20 2014 MATHEMATICA a[n_] := {1, 4, 2}[[Mod[n, 3] + 1]]; Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Jul 19 2013 *) LinearRecurrence[{0, 0, 1}, {1, 4, 2}, 105] (* Ray Chandler, Aug 25 2015 *) PROG (Sage) [power_mod(2, -n, 7)for n in xrange(0, 105)] # Zerinvary Lajos, Jun 07 2009 (Sage) [power_mod(4, n, 7)for n in xrange(0, 105)] # Zerinvary Lajos, Nov 25 2009 (PARI) A153727(n)=[1, 4, 2][n%3+1] \\ M. F. Hasler, Feb 10 2011 (Haskell) a153727 n = a153727_list !! n a153727_list = iterate a006370 1 -- Reinhard Zumkeller, Oct 08 2011 (MAGMA) [2^(-n mod 3) : n in [0..50]]; // Wesley Ivan Hurt, Jun 20 2014 CROSSREFS Cf. A178236 (decimal expansion of (7+sqrt(229))/18). Appears in A179133 (n>=1). Cf. A006370, A080425, A130196, A131534. Sequence in context: A082901 A136619 A132708 * A210937 A016506 A228132 Adjacent sequences:  A153724 A153725 A153726 * A153728 A153729 A153730 KEYWORD nonn,easy AUTHOR Philippe Deléham, Dec 30 2008 STATUS approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)