This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A185453 #33 Dec 12 2023 07:47:37 %S A185453 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 A185453 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 A185453 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 A185453 Trajectory of 1 under repeated application of the map in A185452. %C A185453 Periodic with period length 5. %D A185453 J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, Amer. Math. Soc., 2010; see page 88. %H A185453 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a> %H A185453 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1). %F A185453 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 A185453 f:=n->if n mod 2 = 0 then n/2 else (5*n+1)/2; fi; %p A185453 T:=proc(n,M) global f; local t1,i; t1:=[n]; %p A185453 for i from 1 to M-1 do t1:=[op(t1),f(t1[nops(t1)])]; od: t1; end; %p A185453 T(1,120); %t A185453 NestList[If[EvenQ[#],#/2,(5#+1)/2]&,1,110] (* _Harvey P. Dale_, Jun 24 2011 *) %Y A185453 Cf. A185452, A185454, A185455. %K A185453 nonn %O A185453 1,2 %A A185453 _N. J. A. Sloane_, Feb 04 2011