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%I #52 Mar 08 2024 01:14:27
%S 0,8,1,14,2,20,3,26,4,32,5,38,6,44,7,50,8,56,9,62,10,68,11,74,12,80,
%T 13,86,14,92,15,98,16,104,17,110,18,116,19,122,20,128,21,134,22,140,
%U 23,146,24,152,25,158,26,164,27,170,28,176,29,182,30,188,31,194,32,200,33,206,34,212,35,218,36,224,37
%N a(n) = n/2 if n is even, otherwise 3n+5.
%C Has at least two periodic orbits, {1,8,4,2} and {5,20,10}.
%C Four others are {19,62,31,98,49,152,76,38}, {23,74,37,116,58,29,92,46}, {187,...} and {347,...}. The last two are each of length 44, peaking with 8324 and 10196 respectively. - _Geoffrey H. Morley_, Mar 14 2013
%D J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, Amer. Math. Soc., 2010. See p. 307.
%H Vincenzo Librandi, <a href="/A181762/b181762.txt">Table of n, a(n) for n = 0..2000</a>
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F G.f.: -x*(-8 - x + 2*x^2) / ( (x-1)^2*(1+x)^2 ). - _R. J. Mathar_, Mar 10 2011
%p f:=n->if n mod 2 = 0 then n/2 else 3*x+5 fi;
%t Table[If[EvenQ[n],n/2,3n+5],{n,0,80}] (* _Harvey P. Dale_, Nov 25 2023 *)
%o (Magma) [(7*n+10-10*(-1)^n*(n/2+1))/4: n in [0..80]]; // _Vincenzo Librandi_, May 24 2011
%Y Cf. A006370.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Jan 31 2011
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