%I #33 Dec 12 2023 07:47:37

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

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

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

%N Trajectory of 1 under repeated application of the map in A185452.

%C Periodic with period length 5.

%D J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, Amer. Math. Soc., 2010; see page 88.

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1).

%F G.f.: -x*(1+3*x+8*x^2+4*x^3+2*x^4) / ( (x-1)*(x^4+x^3+x^2+x+1) ). - _R. J. Mathar_, Mar 11 2011

%p f:=n->if n mod 2 = 0 then n/2 else (5*n+1)/2; fi;

%p T:=proc(n,M) global f; local t1,i; t1:=[n];

%p for i from 1 to M-1 do t1:=[op(t1),f(t1[nops(t1)])]; od: t1; end;

%p T(1,120);

%t NestList[If[EvenQ[#],#/2,(5#+1)/2]&,1,110] (* _Harvey P. Dale_, Jun 24 2011 *)

%Y Cf. A185452, A185454, A185455.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Feb 04 2011