A328011 - OEIS

%I #26 Oct 25 2022 01:05:32

%S 1,6,3,16,8,4,2,1,6,3,16,8,4,2,1,6,3,16,8,4,2,1,6,3,16,8,4,2,1,6,3,16,

%T 8,4,2,1,6,3,16,8,4,2,1,6,3,16,8,4,2,1,6,3,16,8,4,2,1,6,3,16,8,4,2,1,

%U 6,3,16,8,4,2,1,6,3,16,8,4,2,1,6,3,16,8,4,2,1

%N The 5x + 1 sequence beginning at 1.

%C See A328010 for further information.

%H Colin Barker, <a href="/A328011/b328011.txt">Table of n, a(n) for n = 0..1000</a>

%H Alex V. Kontorovich & Jeffrey C. Lagarias, <a href="http://arxiv.org/abs/0910.1944">Stochastic Models for the 3x+1 and 5x+1 Problems</a>, arXiv:0910.1944 [math.NT], 2009.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,1).

%F a(n+1) = 5*a(n) + 1 if a(n) is odd, a(n+1) = a(n)/2 otherwise.

%F From _Colin Barker_, Oct 08 2019: (Start)

%F G.f.: (1 + 6*x + 3*x^2 + 16*x^3 + 8*x^4 + 4*x^5 + 2*x^6) / ((1 - x)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).

%F a(n) = a(n-7) for n>6.

%F (End)

%o (PARI) Vec((1 + 6*x + 3*x^2 + 16*x^3 + 8*x^4 + 4*x^5 + 2*x^6) / ((1 - x)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)) + O(x^80)) \\ _Colin Barker_, Oct 08 2019

%Y Cf. A259207, A328010.

%K nonn,easy

%O 0,2

%A _Antoine Beaulieu_, Oct 01 2019