cp's OEIS Frontend

A328010 The 5x + 1 sequence beginning at 17.

%I A328010 #27 Oct 09 2019 10:01:48
%S A328010 17,86,43,216,108,54,27,136,68,34,17,86,43,216,108,54,27,136,68,34,17,
%T A328010 86,43,216,108,54,27,136,68,34,17,86,43,216,108,54,27,136,68,34,17,86,
%U A328010 43,216,108,54,27,136,68,34,17,86,43,216,108,54,27,136,68,34,17
%N A328010 The 5x + 1 sequence beginning at 17.
%C A328010 The 5x+1 problem is similar to the 3x+1 or Collatz problem. For some starting values it is known that the 5x+1 trajectory will tend to infinity or enter a periodic orbit.
%C A328010 Alex V. Kontorovich & Jeffrey C. Lagarias conjectured that there are very few periodic orbits. One of them is shown here.
%C A328010 The two other known periodic orbits are given in the crossrefs.
%H A328010 Colin Barker, <a href="/A328010/b328010.txt">Table of n, a(n) for n = 0..1000</a>
%H A328010 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 A328010 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,1).
%F A328010 a(n+1) = 5*a(n) + 1 if a(n) is odd, a(n+1) = a(n)/2 otherwise.
%F A328010 From _Colin Barker_, Oct 04 2019: (Start)
%F A328010 G.f.: (17 + 86*x + 43*x^2 + 216*x^3 + 108*x^4 + 54*x^5 + 27*x^6 + 136*x^7 + 68*x^8 + 34*x^9) / ((1 - x)*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)).
%F A328010 a(n) = a(n-10) for n>9.
%F A328010 (End)
%o A328010 (PARI) Vec((17 + 86*x + 43*x^2 + 216*x^3 + 108*x^4 + 54*x^5 + 27*x^6 + 136*x^7 + 68*x^8 + 34*x^9) / ((1 - x)*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ _Colin Barker_, Oct 05 2019
%Y A328010 Cf. A259207, A328011.
%K A328010 nonn,easy
%O A328010 0,1
%A A328010 _Antoine Beaulieu_, Oct 01 2019